Daily Papers

Meta-learning has emerged as a powerful approach to train neural networks to learn new tasks quickly from limited data. Broad exposure to different tasks leads to versatile representations enabling general problem solving. But, what are the limits of meta-learning? In this work, we explore the potential of amortizing the most powerful universal predictor, namely Solomonoff Induction (SI), into neural networks via leveraging meta-learning to its limits. We use Universal Turing Machines (UTMs) to generate training data used to expose networks to a broad range of patterns. We provide theoretical analysis of the UTM data generation processes and meta-training protocols. We conduct comprehensive experiments with neural architectures (e.g. LSTMs, Transformers) and algorithmic data generators of varying complexity and universality. Our results suggest that UTM data is a valuable resource for meta-learning, and that it can be used to train neural networks capable of learning universal prediction strategies.

We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a language model can process arbitrarily long inputs using a bounded context. For this purpose, we consider a generalization of autoregressive decoding where, given a long input, emitted tokens are appended to the end of the sequence as the context window advances. We first show that the resulting system corresponds to a classical model of computation, a Lag system, that has long been known to be computationally universal. By leveraging a new proof, we show that a universal Turing machine can be simulated by a Lag system with 2027 production rules. We then investigate whether an existing large language model can simulate the behaviour of such a universal Lag system. We give an affirmative answer by showing that a single system-prompt can be developed for gemini-1.5-pro-001 that drives the model, under deterministic (greedy) decoding, to correctly apply each of the 2027 production rules. We conclude that, by the Church-Turing thesis, prompted gemini-1.5-pro-001 with extended autoregressive (greedy) decoding is a general purpose computer.

We show that transformer-based large language models are computationally universal when augmented with an external memory. Any deterministic language model that conditions on strings of bounded length is equivalent to a finite automaton, hence computationally limited. However, augmenting such models with a read-write memory creates the possibility of processing arbitrarily large inputs and, potentially, simulating any algorithm. We establish that an existing large language model, Flan-U-PaLM 540B, can be combined with an associative read-write memory to exactly simulate the execution of a universal Turing machine, U_{15,2}. A key aspect of the finding is that it does not require any modification of the language model weights. Instead, the construction relies solely on designing a form of stored instruction computer that can subsequently be programmed with a specific set of prompts.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

We evaluated the effectiveness of using language models, that were pre-trained in one domain, as the basis for a classification model in another domain: Dutch book reviews. Pre-trained language models have opened up new possibilities for classification tasks with limited labelled data, because representation can be learned in an unsupervised fashion. In our experiments we have studied the effects of training set size (100-1600 items) on the prediction accuracy of a ULMFiT classifier, based on a language models that we pre-trained on the Dutch Wikipedia. We also compared ULMFiT to Support Vector Machines, which is traditionally considered suitable for small collections. We found that ULMFiT outperforms SVM for all training set sizes and that satisfactory results (~90%) can be achieved using training sets that can be manually annotated within a few hours. We deliver both our new benchmark collection of Dutch book reviews for sentiment classification as well as the pre-trained Dutch language model to the community.

Despite the fact that multilingual agreement (MA) has shown its importance for multilingual neural machine translation (MNMT), current methodologies in the field have two shortages: (i) require parallel data between multiple language pairs, which is not always realistic and (ii) optimize the agreement in an ambiguous direction, which hampers the translation performance. We present Bidirectional Multilingual Agreement via Switched Back-translation (BMA-SBT), a novel and universal multilingual agreement framework for fine-tuning pre-trained MNMT models, which (i) exempts the need for aforementioned parallel data by using a novel method called switched BT that creates synthetic text written in another source language using the translation target and (ii) optimizes the agreement bidirectionally with the Kullback-Leibler Divergence loss. Experiments indicate that BMA-SBT clearly improves the strong baselines on the task of MNMT with three benchmarks: TED Talks, News, and Europarl. In-depth analyzes indicate that BMA-SBT brings additive improvements to the conventional BT method.

The Universal Transformer (UT) is a variant of the Transformer that shares parameters across its layers. Empirical evidence shows that UTs have better compositional generalization than Vanilla Transformers (VTs) in formal language tasks. The parameter-sharing also affords it better parameter efficiency than VTs. Despite its many advantages, scaling UT parameters is much more compute and memory intensive than scaling up a VT. This paper proposes the Sparse Universal Transformer (SUT), which leverages Sparse Mixture of Experts (SMoE) and a new stick-breaking-based dynamic halting mechanism to reduce UT's computation complexity while retaining its parameter efficiency and generalization ability. Experiments show that SUT achieves the same performance as strong baseline models while only using half computation and parameters on WMT'14 and strong generalization results on formal language tasks (Logical inference and CFQ). The new halting mechanism also enables around 50\% reduction in computation during inference with very little performance decrease on formal language tasks.

Since the success of GPT, large language models (LLMs) have been revolutionizing machine learning and have initiated the so-called LLM prompting paradigm. In the era of LLMs, people train a single general-purpose LLM and provide the LLM with different prompts to perform different tasks. However, such empirical success largely lacks theoretical understanding. Here, we present the first theoretical study on the LLM prompting paradigm to the best of our knowledge. In this work, we show that prompting is in fact Turing-complete: there exists a finite-size Transformer such that for any computable function, there exists a corresponding prompt following which the Transformer computes the function. Furthermore, we show that even though we use only a single finite-size Transformer, it can still achieve nearly the same complexity bounds as that of the class of all unbounded-size Transformers. Overall, our result reveals that prompting can enable a single finite-size Transformer to be efficiently universal, which establishes a theoretical underpinning for prompt engineering in practice.

The Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior without explicit knowledge of the system's underlying topology presents a significant challenge, motivating the development of algorithms that can generalize across various grid configurations and boundary conditions. We develop a decoder-only generative pretrained transformer model to solve this problem, showing that our model can simulate Life on a toroidal grid with no prior knowledge on the size of the grid, or its periodic boundary conditions (LifeGPT). LifeGPT is topology-agnostic with respect to its training data and our results show that a GPT model is capable of capturing the deterministic rules of a Turing-complete system with near-perfect accuracy, given sufficiently diverse training data. We also introduce the idea of an `autoregressive autoregressor' to recursively implement Life using LifeGPT. Our results pave the path towards true universal computation within a large language model (LLM) framework, synthesizing of mathematical analysis with natural language processing, and probing AI systems for situational awareness about the evolution of such algorithms without ever having to compute them. Similar GPTs could potentially solve inverse problems in multicellular self-assembly by extracting CA-compatible rulesets from real-world biological systems to create new predictive models, which would have significant consequences for the fields of bioinspired materials, tissue engineering, and architected materials design.

We propose Token Turing Machines (TTM), a sequential, autoregressive Transformer model with memory for real-world sequential visual understanding. Our model is inspired by the seminal Neural Turing Machine, and has an external memory consisting of a set of tokens which summarise the previous history (i.e., frames). This memory is efficiently addressed, read and written using a Transformer as the processing unit/controller at each step. The model's memory module ensures that a new observation will only be processed with the contents of the memory (and not the entire history), meaning that it can efficiently process long sequences with a bounded computational cost at each step. We show that TTM outperforms other alternatives, such as other Transformer models designed for long sequences and recurrent neural networks, on two real-world sequential visual understanding tasks: online temporal activity detection from videos and vision-based robot action policy learning. Code is publicly available at: https://github.com/google-research/scenic/tree/main/scenic/projects/token_turing

In this article we prove that the general transformer neural model undergirding modern large language models (LLMs) is Turing complete under reasonable assumptions. This is the first work to directly address the Turing completeness of the underlying technology employed in GPT-x as past work has focused on the more expressive, full auto-encoder transformer architecture. From this theoretical analysis, we show that the sparsity/compressibility of the word embedding is an important consideration for Turing completeness to hold. We also show that Transformers are are a variant of B machines studied by Hao Wang.

Intermediate reasoning or acting steps have successfully improved large language models (LLMs) for handling various downstream natural language processing (NLP) tasks. When applying LLMs for code generation, recent works mainly focus on directing the models to articulate intermediate natural-language reasoning steps, as in chain-of-thought (CoT) prompting, and then output code with the natural language or other structured intermediate steps. However, such output is not suitable for code translation or generation tasks since the standard CoT has different logical structures and forms of expression with the code. In this work, we introduce the universal code (UniCode) as the intermediate representation. It is a description of algorithm steps using a mix of conventions of programming languages, such as assignment operator, conditional operator, and loop. Hence, we collect an instruction dataset UniCoder-Instruct to train our model UniCoder on multi-task learning objectives. UniCoder-Instruct comprises natural-language questions, code solutions, and the corresponding universal code. The alignment between the intermediate universal code representation and the final code solution significantly improves the quality of the generated code. The experimental results demonstrate that UniCoder with the universal code significantly outperforms the previous prompting methods by a large margin, showcasing the effectiveness of the structural clues in pseudo-code.

Self-consistency with chain-of-thought prompting (CoT) has demonstrated remarkable performance gains on various challenging tasks, by utilizing multiple reasoning paths sampled from large language models (LLMs). However, self-consistency relies on the answer extraction process to aggregate multiple solutions, which is not applicable to free-form answers. In this work, we propose Universal Self-Consistency (USC), which leverages LLMs themselves to select the most consistent answer among multiple candidates. We evaluate USC on a variety of benchmarks, including mathematical reasoning, code generation, long-context summarization, and open-ended question answering. On open-ended generation tasks where the original self-consistency method is not applicable, USC effectively utilizes multiple samples and improves the performance. For mathematical reasoning, USC matches the standard self-consistency performance without requiring the answer formats to be similar. Finally, without access to execution results, USC also matches the execution-based voting performance on code generation.

Researchers are investing substantial effort in developing powerful general-purpose agents, wherein Foundation Models are used as modules within agentic systems (e.g. Chain-of-Thought, Self-Reflection, Toolformer). However, the history of machine learning teaches us that hand-designed solutions are eventually replaced by learned solutions. We formulate a new research area, Automated Design of Agentic Systems (ADAS), which aims to automatically create powerful agentic system designs, including inventing novel building blocks and/or combining them in new ways. We further demonstrate that there is an unexplored yet promising approach within ADAS where agents can be defined in code and new agents can be automatically discovered by a meta agent programming ever better ones in code. Given that programming languages are Turing Complete, this approach theoretically enables the learning of any possible agentic system: including novel prompts, tool use, control flows, and combinations thereof. We present a simple yet effective algorithm named Meta Agent Search to demonstrate this idea, where a meta agent iteratively programs interesting new agents based on an ever-growing archive of previous discoveries. Through extensive experiments across multiple domains including coding, science, and math, we show that our algorithm can progressively invent agents with novel designs that greatly outperform state-of-the-art hand-designed agents. Importantly, we consistently observe the surprising result that agents invented by Meta Agent Search maintain superior performance even when transferred across domains and models, demonstrating their robustness and generality. Provided we develop it safely, our work illustrates the potential of an exciting new research direction toward automatically designing ever-more powerful agentic systems to benefit humanity.

Large language models (LLMs) have demonstrated remarkable generalizability, such as understanding arbitrary entities and relations. Instruction tuning has proven effective for distilling LLMs into more cost-efficient models such as Alpaca and Vicuna. Yet such student models still trail the original LLMs by large margins in downstream applications. In this paper, we explore targeted distillation with mission-focused instruction tuning to train student models that can excel in a broad application class such as open information extraction. Using named entity recognition (NER) for case study, we show how ChatGPT can be distilled into much smaller UniversalNER models for open NER. For evaluation, we assemble the largest NER benchmark to date, comprising 43 datasets across 9 diverse domains such as biomedicine, programming, social media, law, finance. Without using any direct supervision, UniversalNER attains remarkable NER accuracy across tens of thousands of entity types, outperforming general instruction-tuned models such as Alpaca and Vicuna by over 30 absolute F1 points in average. With a tiny fraction of parameters, UniversalNER not only acquires ChatGPT's capability in recognizing arbitrary entity types, but also outperforms its NER accuracy by 7-9 absolute F1 points in average. Remarkably, UniversalNER even outperforms by a large margin state-of-the-art multi-task instruction-tuned systems such as InstructUIE, which uses supervised NER examples. We also conduct thorough ablation studies to assess the impact of various components in our distillation approach. We will release the distillation recipe, data, and UniversalNER models to facilitate future research on targeted distillation.

Fuzzing has achieved tremendous success in discovering bugs and vulnerabilities in various software systems. Systems under test (SUTs) that take in programming or formal language as inputs, e.g., compilers, runtime engines, constraint solvers, and software libraries with accessible APIs, are especially important as they are fundamental building blocks of software development. However, existing fuzzers for such systems often target a specific language, and thus cannot be easily applied to other languages or even other versions of the same language. Moreover, the inputs generated by existing fuzzers are often limited to specific features of the input language, and thus can hardly reveal bugs related to other or new features. This paper presents Fuzz4All, the first fuzzer that is universal in the sense that it can target many different input languages and many different features of these languages. The key idea behind Fuzz4All is to leverage large language models (LLMs) as an input generation and mutation engine, which enables the approach to produce diverse and realistic inputs for any practically relevant language. To realize this potential, we present a novel autoprompting technique, which creates LLM prompts that are wellsuited for fuzzing, and a novel LLM-powered fuzzing loop, which iteratively updates the prompt to create new fuzzing inputs. We evaluate Fuzz4All on nine systems under test that take in six different languages (C, C++, Go, SMT2, Java and Python) as inputs. The evaluation shows, across all six languages, that universal fuzzing achieves higher coverage than existing, language-specific fuzzers. Furthermore, Fuzz4All has identified 76 bugs in widely used systems, such as GCC, Clang, Z3, CVC5, OpenJDK, and the Qiskit quantum computing platform, with 47 bugs already confirmed by developers as previously unknown.

Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When dealing with arithmetic tasks, LLMs often memorize specific examples rather than learning the underlying computational logic, limiting their ability to generalize to new problems. In this paper, we propose a Composable Arithmetic Execution Framework (CAEF) that enables LLMs to learn to execute step-by-step computations by emulating Turing Machines, thereby gaining a genuine understanding of computational logic. Moreover, the proposed framework is highly scalable, allowing composing learned operators to significantly reduce the difficulty of learning complex operators. In our evaluation, CAEF achieves nearly 100% accuracy across seven common mathematical operations on the LLaMA 3.1-8B model, effectively supporting computations involving operands with up to 100 digits, a level where GPT-4o falls short noticeably in some settings.

Large Language Models (LLMs) are popular for their impressive abilities, but the need for model-specific fine-tuning or task-specific prompt engineering can hinder their generalization. We propose UPRISE (Universal Prompt Retrieval for Improving zero-Shot Evaluation), which tunes a lightweight and versatile retriever that automatically retrieves prompts for a given zero-shot task input. Specifically, we demonstrate universality in a cross-task and cross-model scenario: the retriever is tuned on a diverse set of tasks, but tested on unseen task types; we use a small frozen LLM, GPT-Neo-2.7B, for tuning the retriever, but test the retriever on different LLMs of much larger scales, such as BLOOM-7.1B, OPT-66B and GPT3-175B. Additionally, we show that UPRISE mitigates the hallucination problem in our experiments with ChatGPT, suggesting its potential to improve even the strongest LLMs. Our model and code are available at https://github.com/microsoft/LMOps.

Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in mathematical reasoning capabilities. We postulate that the inherent nature of LLM training, which focuses on predicting probabilities of next token, presents challenges in effectively modeling mathematical reasoning that demands exact calculations, both from data-driven and theoretical standpoints. In this paper, we address this challenge by enriching the data landscape and introducing a novel math dataset, enhanced with a capability to utilize a Python code interpreter. This dataset is derived from GSM8K and MATH and has been further refined through a combination of GPT-4 annotations, human review, and self-training processes, where the errors in the original GSM8K training set have been fixed. Additionally, we propose a tentative, easily replicable protocol for the fine-tuning of math-specific LLMs, which has led to a significant improvement in the performance of a 7B-parameter LLM on the GSM8K and MATH datasets. We are committed to advancing the field of mathematical reasoning in LLMs and, to that end, we have made the model checkpoints and will make the dataset publicly available. We hope this will facilitate further research and development within the community.

Large language models (LLMs) with memory are computationally universal. However, mainstream LLMs are not taking full advantage of memory, and the designs are heavily influenced by biological brains. Due to their approximate nature and proneness to the accumulation of errors, conventional neural memory mechanisms cannot support LLMs to simulate complex reasoning. In this paper, we seek inspiration from modern computer architectures to augment LLMs with symbolic memory for complex multi-hop reasoning. Such a symbolic memory framework is instantiated as an LLM and a set of SQL databases, where the LLM generates SQL instructions to manipulate the SQL databases. We validate the effectiveness of the proposed memory framework on a synthetic dataset requiring complex reasoning. The project website is available at https://chatdatabase.github.io/ .

We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.

Large deep learning models offer significant accuracy gains, but training billions to trillions of parameters is challenging. Existing solutions such as data and model parallelisms exhibit fundamental limitations to fit these models into limited device memory, while obtaining computation, communication and development efficiency. We develop a novel solution, Zero Redundancy Optimizer (ZeRO), to optimize memory, vastly improving training speed while increasing the model size that can be efficiently trained. ZeRO eliminates memory redundancies in data- and model-parallel training while retaining low communication volume and high computational granularity, allowing us to scale the model size proportional to the number of devices with sustained high efficiency. Our analysis on memory requirements and communication volume demonstrates: ZeRO has the potential to scale beyond 1 Trillion parameters using today's hardware. We implement and evaluate ZeRO: it trains large models of over 100B parameter with super-linear speedup on 400 GPUs, achieving throughput of 15 Petaflops. This represents an 8x increase in model size and 10x increase in achievable performance over state-of-the-art. In terms of usability, ZeRO can train large models of up to 13B parameters (e.g., larger than Megatron GPT 8.3B and T5 11B) without requiring model parallelism which is harder for scientists to apply. Last but not the least, researchers have used the system breakthroughs of ZeRO to create the world's largest language model (Turing-NLG, 17B parameters) with record breaking accuracy.

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence, capable of processing and understanding extensive human knowledge to enhance problem-solving across various domains. This paper explores the potential of LLMs to drive the discovery of symbolic solutions within scientific and engineering disciplines, where such solutions are crucial for advancing theoretical and practical applications. We propose a novel framework that utilizes LLMs in an evolutionary search methodology, augmented by a dynamic knowledge library that integrates and refines insights in an open-ended manner. This approach aims to tackle the dual challenges of efficiently navigating complex symbolic representation spaces and leveraging both existing and newly generated knowledge to foster open-ended innovation. By enabling LLMs to interact with and expand upon a knowledge library, we facilitate the continuous generation of novel solutions in diverse forms such as language, code, and mathematical expressions. Our experimental results demonstrate that this method not only enhances the efficiency of searching for symbolic solutions but also supports the ongoing discovery process, akin to human scientific endeavors. This study represents a first effort in conceptualizing the search for symbolic solutions as a lifelong, iterative process, marking a significant step towards harnessing AI in the perpetual pursuit of scientific and engineering breakthroughs. We have open-sourced our code and data, please visit https://github.com/pgg3/CoEvo for more information.

In the burgeoning field of artificial intelligence (AI), the unprecedented progress of large language models (LLMs) in natural language processing (NLP) offers an opportunity to revisit the entire approach of traditional metrics of machine intelligence, both in form and content. As the realm of machine cognitive evaluation has already reached Imitation, the next step is an efficient Language Acquisition and Understanding. Our paper proposes a paradigm shift from the established Turing Test towards an all-embracing framework that hinges on language acquisition, taking inspiration from the recent advancements in LLMs. The present contribution is deeply tributary of the excellent work from various disciplines, point out the need to keep interdisciplinary bridges open, and delineates a more robust and sustainable approach.

Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap (Delta), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large Delta values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and Delta = 0. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.

Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarce, often perceived as an act of mathematical genius by great mathematicians such as Ramanujan, Euler, and Gauss. Recent efforts to automate the discovery of formulas for mathematical constants, such as the Ramanujan Machine project, relied on exhaustive search. Despite several successful discoveries, exhaustive search remains limited by the space of options that can be covered and by the need for vast amounts of computational resources. Here we propose a fundamentally different method to search for conjectures on mathematical constants: through analysis of integer sequences. We introduce the Enumerated Signed-continued-fraction Massey Approve (ESMA) algorithm, which builds on the Berlekamp-Massey algorithm to identify patterns in integer sequences that represent mathematical constants. The ESMA algorithm found various known formulas for e, e^2, tan(1), and ratios of values of Bessel functions. The algorithm further discovered a large number of new conjectures for these constants, some providing simpler representations and some providing faster numerical convergence than the corresponding simple continued fractions. Along with the algorithm, we present mathematical tools for manipulating continued fractions. These connections enable us to characterize what space of constants can be found by ESMA and quantify its algorithmic advantage in certain scenarios. Altogether, this work continues in the development of augmenting mathematical intuition by computer algorithms, to help reveal mathematical structures and accelerate mathematical research.

Existing checkpointing approaches seem ill-suited for distributed training even though hardware limitations make model parallelism, i.e., sharding model state across multiple accelerators, a requirement for model scaling. Consolidating distributed model state into a single checkpoint unacceptably slows down training, and is impractical at extreme scales. Distributed checkpoints, in contrast, are tightly coupled to the model parallelism and hardware configurations of the training run, and thus unusable on different configurations. To address this problem, we propose Universal Checkpointing, a technique that enables efficient checkpoint creation while providing the flexibility of resuming on arbitrary parallelism strategy and hardware configurations. Universal Checkpointing unlocks unprecedented capabilities for large-scale training such as improved resilience to hardware failures through continued training on remaining healthy hardware, and reduced training time through opportunistic exploitation of elastic capacity. The key insight of Universal Checkpointing is the selection of the optimal representation in each phase of the checkpointing life cycle: distributed representation for saving, and consolidated representation for loading. This is achieved using two key mechanisms. First, the universal checkpoint format, which consists of a consolidated representation of each model parameter and metadata for mapping parameter fragments into training ranks of arbitrary model-parallelism configuration. Second, the universal checkpoint language, a simple but powerful specification language for converting distributed checkpoints into the universal checkpoint format. Our evaluation demonstrates the effectiveness and generality of Universal Checkpointing on state-of-the-art model architectures and a wide range of parallelism techniques.

Instruction tuning -- fine-tuning a large language model (LLM) on pairs of instructions and desired outcomes -- is an approach that enables pre-trained language models to perform real-world tasks and follow human instructions. Its practical success depends on the model learning a broader set of instructions than those it was trained on. Yet the factors that determine model generalization to such unseen tasks are not well understood. %To understand the driving factors of generalization, In this paper, we experiment with string rewrites, a symbolic task that serves as a building block for Turing complete Markov algorithms while allowing experimental control of "inputs" and "instructions". We investigate the trade-off between the number of instructions the model is trained on and the number of training samples provided for each instruction and observe that the diversity of the instruction set determines generalization. Generalization emerges once a diverse enough set of tasks is provided, even though very few examples are provided for each task. Instruction diversity also ensures robustness with respect to non-uniform distributions of instructions in the training set.

Underlying data distributions of natural language, programming code, and mathematical symbols vary vastly, presenting a complex challenge for large language models (LLMs) that strive to achieve high performance across all three domains simultaneously. Achieving a very high level of proficiency for an LLM within a specific domain often requires extensive training with relevant corpora, which is typically accompanied by a sacrifice in performance in other domains. In this paper, we propose to fuse models that are already highly-specialized directly. The proposed fusing framework, UltraFuser, consists of three distinct specialists that are already sufficiently trained on language, coding, and mathematics. A token-level gating mechanism is introduced to blend the specialists' outputs. A two-stage training strategy accompanied by balanced sampling is designed to ensure stability. To effectively train the fused model, we further construct a high-quality supervised instruction tuning dataset, UltraChat 2, which includes text, code, and mathematical content. This dataset comprises approximately 300,000 instructions and covers a wide range of topics in each domain. Experiments show that our model could simultaneously achieve mastery of the three crucial domains.

We contribute to the study of formal languages that can be recognized by transformer encoders. We focus on two self-attention mechanisms: (1) UHAT (Unique Hard Attention Transformers) and (2) AHAT (Average Hard Attention Transformers). UHAT encoders are known to recognize only languages inside the circuit complexity class {sf AC}^0, i.e., accepted by a family of poly-sized and depth-bounded boolean circuits with unbounded fan-ins. On the other hand, AHAT encoders can recognize languages outside {sf AC}^0), but their expressive power still lies within the bigger circuit complexity class {sf TC}^0, i.e., {sf AC}^0-circuits extended by majority gates. We first show a negative result that there is an {sf AC}^0-language that cannot be recognized by an UHAT encoder. On the positive side, we show that UHAT encoders can recognize a rich fragment of {sf AC}^0-languages, namely, all languages definable in first-order logic with arbitrary unary numerical predicates. This logic, includes, for example, all regular languages from {sf AC}^0. We then show that AHAT encoders can recognize all languages of our logic even when we enrich it with counting terms. We apply these results to derive new results on the expressive power of UHAT and AHAT up to permutation of letters (a.k.a. Parikh images).

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

Chomsky and others have very directly claimed that large language models (LLMs) are equally capable of learning languages that are possible and impossible for humans to learn. However, there is very little published experimental evidence to support such a claim. Here, we develop a set of synthetic impossible languages of differing complexity, each designed by systematically altering English data with unnatural word orders and grammar rules. These languages lie on an impossibility continuum: at one end are languages that are inherently impossible, such as random and irreversible shuffles of English words, and on the other, languages that may not be intuitively impossible but are often considered so in linguistics, particularly those with rules based on counting word positions. We report on a wide range of evaluations to assess the capacity of GPT-2 small models to learn these uncontroversially impossible languages, and crucially, we perform these assessments at various stages throughout training to compare the learning process for each language. Our core finding is that GPT-2 struggles to learn impossible languages when compared to English as a control, challenging the core claim. More importantly, we hope our approach opens up a productive line of inquiry in which different LLM architectures are tested on a variety of impossible languages in an effort to learn more about how LLMs can be used as tools for these cognitive and typological investigations.

Turing machine and decision tree have developed independently for a long time. With the recent development of differentiable models, there is an intersection between them. Neural turing machine(NTM) opens door for the memory network. It use differentiable attention mechanism to read/write external memory bank. Differentiable forest brings differentiable properties to classical decision tree. In this short note, we show the deep connection between these two models. That is: differentiable forest is a special case of NTM. Differentiable forest is actually decision tree based neural turing machine. Based on this deep connection, we propose a response augmented differential forest (RaDF). The controller of RaDF is differentiable forest, the external memory of RaDF are response vectors which would be read/write by leaf nodes.

The standard methodology of evaluating large language models (LLMs) based on static pairs of inputs and outputs is insufficient for developing assistants: this kind of assessments fails to take into account the essential interactive element in their deployment, and therefore limits how we understand language model capabilities. We introduce CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We conduct a study with CheckMate to evaluate three language models~(InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a preliminary taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we identify useful scenarios and existing issues of GPT-4 in mathematical reasoning through a series of case studies contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models which communicate uncertainty, respond well to user corrections, are more interpretable and concise may constitute better assistants; interactive evaluation is a promising way to continually navigate the capability of these models; humans should be aware of language models' algebraic fallibility, and for that reason discern where they should be used.

Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than computability in philosophical and AI problems. Second, to rephrase the notion of computability in terms of solvability, i.e. treating computability as non-sufficient for establishing intelligence. The Church-Turing thesis is therefore revisited and rephrased in order to capture the ontological background of spatial and temporal complexity. Third, to emphasize ontological differences between different time complexities, which seem to provide a solid base towards better understanding of artificial intelligence in general.

Large language models (LLMs), as epitomized by models like ChatGPT, have revolutionized the field of natural language processing (NLP). Along with this trend, code-based large language models such as StarCoder, WizardCoder, and CodeLlama have emerged, trained extensively on vast repositories of code data. Yet, inherent in their design, these models primarily focus on generative tasks like code generation, code completion, and comment generation, and general support for multiple programming languages. While the generic abilities of code LLMs are useful for many programmers, the area of high-performance computing (HPC) has a narrower set of requirements that make a smaller and more domain-specific LM a smarter choice. This paper introduces OMPGPT, a novel model meticulously designed to harness the inherent strengths of language models for OpenMP pragma generation. Furthermore, we adopt and adapt prompt engineering techniques from the NLP domain to create chain-of-OMP, an innovative strategy designed to enhance OMPGPT's effectiveness. Our extensive evaluations demonstrate that OMPGPT outperforms existing large language models specialized in OpenMP tasks and maintains a notably smaller size, aligning it more closely with the typical hardware constraints of HPC environments. We consider our contribution as a pivotal bridge, connecting the advantage of language models with the specific demands of HPC tasks. The success of OMPGPT lays a solid foundation, suggesting its potential applicability and adaptability to a wider range of HPC tasks, thereby opening new avenues in the field of computational efficiency and effectiveness.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

The Omega numbers-the halting probabilities of universal prefix-free machines-are known to be exactly the Martin-L{\"o}f random left-c.e. reals. We show that one cannot uniformly produce, from a Martin-L{\"o}f random left-c.e. real alpha, a universal prefix-free machine U whose halting probability is alpha. We also answer a question of Barmpalias and Lewis-Pye by showing that given a left-c.e. real alpha, one cannot uniformly produce a left-c.e. real beta such that alpha -- beta is neither left-c.e. nor right-c.e.

The evaluation of mathematical reasoning capabilities is essential for advancing Artificial General Intelligence (AGI). While Large Language Models (LLMs) have shown impressive performance in solving mathematical problems, existing benchmarks such as GSM8K and MATH present limitations, including narrow problem definitions with specific numbers and reliance on predetermined rules that hinder accurate assessments of reasoning and adaptability. This paper introduces the UTMath Benchmark, which robustly evaluates the models through extensive unit tests. It consists of 1,053 problems across 9 mathematical domains, with over 68 test cases per problem. We propose an innovative evaluation framework inspired by unit testing in software development, focusing on both accuracy and reliability of results. Furthermore, we introduce the Reasoning-to-Coding of Thoughts (RCoT) approach, which encourages LLMs to perform explicit reasoning before generating code, leading to generating more advanced solution and improved performance. Furthermore, we are releasing not only the UTMath benchmark but also the UTMath-Train training dataset (more than 70k samples), to support the community in further exploring mathematical reasoning.

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate language models (LMs). In this paper, we introduce the USACO benchmark with 307 problems from the USA Computing Olympiad, along with high-quality unit tests, reference code, and official analyses for each problem. These resources enable us to construct and test a range of LM inference methods for competitive programming for the first time. We find GPT-4 only achieves a 8.7% pass@1 accuracy with zero-shot chain-of-thought prompting, and our best inference method improves it to 20.2% using a combination of self-reflection and retrieval over episodic knowledge. However, this is far from solving the benchmark. To better understand the remaining challenges, we design a novel human-in-the-loop study and surprisingly find that a small number of targeted hints enable GPT-4 to solve 13 out of 15 problems previously unsolvable by any model and method. Our benchmark, baseline methods, quantitative results, and qualitative analysis serve as an initial step toward LMs with grounded, creative, and algorithmic reasoning.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

Recently, considerable efforts have been directed towards compressing Large Language Models (LLMs), which showcase groundbreaking capabilities across diverse applications but entail significant deployment costs due to their large sizes. Meanwhile, much less attention has been given to mitigating the costs associated with deploying multiple LLMs of varying sizes despite its practical significance. Thus, this paper introduces any-precision LLM, extending the concept of any-precision DNN to LLMs. Addressing challenges in any-precision LLM, we propose a lightweight method for any-precision quantization of LLMs, leveraging a post-training quantization framework, and develop a specialized software engine for its efficient serving. As a result, our solution significantly reduces the high costs of deploying multiple, different-sized LLMs by overlaying LLMs quantized to varying bit-widths, such as 3, 4, ..., n bits, into a memory footprint comparable to a single n-bit LLM. All the supported LLMs with varying bit-widths demonstrate state-of-the-art model quality and inference throughput, proving itself to be a compelling option for deployment of multiple, different-sized LLMs. The source code will be publicly available soon.

The Languini Kitchen serves as both a research collective and codebase designed to empower researchers with limited computational resources to contribute meaningfully to the field of language modelling. We introduce an experimental protocol that enables model comparisons based on equivalent compute, measured in accelerator hours. The number of tokens on which a model is trained is defined by the model's throughput and the chosen compute class. Notably, this approach avoids constraints on critical hyperparameters which affect total parameters or floating-point operations. For evaluation, we pre-process an existing large, diverse, and high-quality dataset of books that surpasses existing academic benchmarks in quality, diversity, and document length. On it, we compare methods based on their empirical scaling trends which are estimated through experiments at various levels of compute. This work also provides two baseline models: a feed-forward model derived from the GPT-2 architecture and a recurrent model in the form of a novel LSTM with ten-fold throughput. While the GPT baseline achieves better perplexity throughout all our levels of compute, our LSTM baseline exhibits a predictable and more favourable scaling law. This is due to the improved throughput and the need for fewer training tokens to achieve the same decrease in test perplexity. Extrapolating the scaling laws leads of both models results in an intersection at roughly 50,000 accelerator hours. We hope this work can serve as the foundation for meaningful and reproducible language modelling research.

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education.

The reasoning capabilities of advanced large language models (LLMs) like o1 have revolutionized artificial intelligence applications. Nevertheless, evaluating and optimizing complex reasoning processes remain significant challenges due to diverse policy distributions and the inherent limitations of human effort and accuracy. In this paper, we present AURORA, a novel automated framework for training universal process reward models (PRMs) using ensemble prompting and reverse verification. The framework employs a two-phase approach: First, it uses diverse prompting strategies and ensemble methods to perform automated annotation and evaluation of processes, ensuring robust assessments for reward learning. Second, it leverages practical reference answers for reverse verification, enhancing the model's ability to validate outputs and improving training accuracy. To assess the framework's performance, we extend beyond the existing ProcessBench benchmark by introducing UniversalBench, which evaluates reward predictions across full trajectories under diverse policy distribtion with long Chain-of-Thought (CoT) outputs. Experimental results demonstrate that AURORA enhances process evaluation accuracy, improves PRMs' accuracy for diverse policy distributions and long-CoT responses. The project will be open-sourced at https://auroraprm.github.io/. The Universal-PRM-7B is available at https://huggingface.co/infly/Universal-PRM-7B.

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

Given that Large Language Models (LLMs) have made significant progress in writing code, can they now be used to autonomously reproduce results from research repositories? Such a capability would be a boon to the research community, helping researchers validate, understand, and extend prior work. To advance towards this goal, we introduce SUPER, the first benchmark designed to evaluate the capability of LLMs in setting up and executing tasks from research repositories. SUPERaims to capture the realistic challenges faced by researchers working with Machine Learning (ML) and Natural Language Processing (NLP) research repositories. Our benchmark comprises three distinct problem sets: 45 end-to-end problems with annotated expert solutions, 152 sub problems derived from the expert set that focus on specific challenges (e.g., configuring a trainer), and 602 automatically generated problems for larger-scale development. We introduce various evaluation measures to assess both task success and progress, utilizing gold solutions when available or approximations otherwise. We show that state-of-the-art approaches struggle to solve these problems with the best model (GPT-4o) solving only 16.3% of the end-to-end set, and 46.1% of the scenarios. This illustrates the challenge of this task, and suggests that SUPER can serve as a valuable resource for the community to make and measure progress.

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

Instruction-following made modern large language models (LLMs) helpful assistants. However, the key to taming LLMs on complex instructions remains mysterious, for that there are huge gaps between models trained by open-source community and those trained by leading companies. To bridge the gap, we propose a simple and scalable approach UltraIF for building LLMs that can follow complex instructions with open-source data. UltraIF first decomposes real-world user prompts into simpler queries, constraints, and corresponding evaluation questions for the constraints. Then, we train an UltraComposer to compose constraint-associated prompts with evaluation questions. This prompt composer allows us to synthesize complicated instructions as well as filter responses with evaluation questions. In our experiment, for the first time, we successfully align LLaMA-3.1-8B-Base to catch up with its instruct version on 5 instruction-following benchmarks without any benchmark information, using only 8B model as response generator and evaluator. The aligned model also achieved competitive scores on other benchmarks. Moreover, we also show that UltraIF could further improve LLaMA-3.1-8B-Instruct through self-alignment, motivating broader use cases for the method. Our code will be available at https://github.com/kkk-an/UltraIF.

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (\eg, LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called {MetaMathQA}. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (\ie, GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, {MetaMath-70B} achieves an accuracy of 82.3% on {GSM8K}, slightly better than {GPT-3.5-Turbo}. We release the {MetaMathQA} dataset, the {MetaMath} models with different model sizes and the training code for public use.

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. Afterward, we analyze the variety of self-improvement strategies proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We critically consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox.

Can Transformers predict new syllogisms by composing established ones? More generally, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity, but this does not address the learnability objective. This paper puts forward the notion of 'globality degree' of a target distribution to capture when weak learning is efficiently achievable by regular Transformers, where the latter measures the least number of tokens required in addition to the tokens histogram to correlate nontrivially with the target. As shown experimentally and theoretically under additional assumptions, distributions with high globality cannot be learned efficiently. In particular, syllogisms cannot be composed on long chains. Furthermore, we show that (i) an agnostic scratchpad cannot help to break the globality barrier, (ii) an educated scratchpad can help if it breaks the globality at each step, however not all such scratchpads can generalize to out-of-distribution (OOD) samples, (iii) a notion of 'inductive scratchpad', that composes the prior information more efficiently, can both break the globality barrier and improve the OOD generalization. In particular, some inductive scratchpads can achieve length generalizations of up to 6x for some arithmetic tasks depending on the input formatting.

Recent progress in large-scale language models has enabled breakthroughs in previously intractable computer programming tasks. Prior work in meta-learning and neural architecture search has led to substantial successes across various task domains, spawning myriad approaches for algorithmically optimizing the design and learning dynamics of deep learning models. At the intersection of these research areas, we implement a code-generating language model with the ability to modify its own source code. Self-programming AI algorithms have been of interest since the dawn of AI itself. Although various theoretical formulations of generalized self-programming AI have been posed, no such system has been successfully implemented to date under real-world computational constraints. Applying AI-based code generation to AI itself, we develop and experimentally validate the first practical implementation of a self-programming AI system. We empirically show that a self-programming AI implemented using a code generation model can successfully modify its own source code to improve performance and program sub-models to perform auxiliary tasks. Our model can self-modify various properties including model architecture, computational capacity, and learning dynamics.

Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs. However, existing methods for large-scale dataset creation require substantial seed data and high computational costs for data synthesis, posing significant challenges for scalability. We introduce InfinityMATH, a scalable instruction tuning dataset for programmatic mathematical reasoning. The construction pipeline emphasizes decoupling numbers from mathematical problems to synthesize number-independent programs, enabling efficient and flexible scaling while minimizing dependency on specific numerical values. Fine-tuning experiments with open-source language and code models, such as Llama2 and CodeLlama, demonstrate the practical benefits of InfinityMATH. These fine-tuned models, showed significant relative improvements on both in-domain and out-of-domain benchmarks, ranging from 184.7% to 514.3% on average. Additionally, these models exhibited high robustness on the GSM8K+ and MATH+ benchmarks, which are enhanced version of test sets with simply the number variations. InfinityMATH ensures that models are more versatile and effective across a broader range of mathematical problems. The data is available at https://huggingface.co/datasets/flagopen/InfinityMATH.

Foundation Large Language Models (LLMs) such as GPT-4 represent a revolution in AI due to their real-world applications though natural language processing. However, they also pose many significant risks such as the presence of biased, private, or harmful text, and the unauthorized inclusion of copyrighted material. We introduce h2oGPT, a suite of open-source code repositories for the creation and use of Large Language Models (LLMs) based on Generative Pretrained Transformers (GPTs). The goal of this project is to create the world's best truly open-source alternative to closed-source GPTs. In collaboration with and as part of the incredible and unstoppable open-source community, we open-source several fine-tuned h2oGPT models from 7 to 40 Billion parameters, ready for commercial use under fully permissive Apache 2.0 licenses. Included in our release is 100% private document search using natural language. Open-source language models help boost AI development and make it more accessible and trustworthy. They lower entry hurdles, allowing people and groups to tailor these models to their needs. This openness increases innovation, transparency, and fairness. An open-source strategy is needed to share AI benefits fairly, and H2O.ai will continue to democratize AI and LLMs.

Artificial intelligence (AI) researchers have been developing and refining large language models (LLMs) that exhibit remarkable capabilities across a variety of domains and tasks, challenging our understanding of learning and cognition. The latest model developed by OpenAI, GPT-4, was trained using an unprecedented scale of compute and data. In this paper, we report on our investigation of an early version of GPT-4, when it was still in active development by OpenAI. We contend that (this early version of) GPT-4 is part of a new cohort of LLMs (along with ChatGPT and Google's PaLM for example) that exhibit more general intelligence than previous AI models. We discuss the rising capabilities and implications of these models. We demonstrate that, beyond its mastery of language, GPT-4 can solve novel and difficult tasks that span mathematics, coding, vision, medicine, law, psychology and more, without needing any special prompting. Moreover, in all of these tasks, GPT-4's performance is strikingly close to human-level performance, and often vastly surpasses prior models such as ChatGPT. Given the breadth and depth of GPT-4's capabilities, we believe that it could reasonably be viewed as an early (yet still incomplete) version of an artificial general intelligence (AGI) system. In our exploration of GPT-4, we put special emphasis on discovering its limitations, and we discuss the challenges ahead for advancing towards deeper and more comprehensive versions of AGI, including the possible need for pursuing a new paradigm that moves beyond next-word prediction. We conclude with reflections on societal influences of the recent technological leap and future research directions.

We introduce WebApp1K, a practical code-generation benchmark to measure LLM ability to develop web apps. This benchmark aims to calibrate LLM output and aid the models to progressively improve code correctness and functionality. The benchmark is lightweight and easy to run. We present the initial version of WebApp1K, and share our findings of running the benchmark against the latest frontier LLMs. First, open source LLMs deliver impressive performance, closely trailing behind GPT-4o and Claude 3.5. Second, model size has strong correlation with code correctness. Third, no prompting techniques have been found to lift performance either universally to all models, or significantly to a single model.

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

The advancement in generative AI could be boosted with more accessible mathematics. Beyond human-AI chat, large language models (LLMs) are emerging in programming, algorithm discovery, and theorem proving, yet their genomics application is limited. This project introduces Math Agents and mathematical embedding as fresh entries to the "Moore's Law of Mathematics", using a GPT-based workflow to convert equations from literature into LaTeX and Python formats. While many digital equation representations exist, there's a lack of automated large-scale evaluation tools. LLMs are pivotal as linguistic user interfaces, providing natural language access for human-AI chat and formal languages for large-scale AI-assisted computational infrastructure. Given the infinite formal possibility spaces, Math Agents, which interact with math, could potentially shift us from "big data" to "big math". Math, unlike the more flexible natural language, has properties subject to proof, enabling its use beyond traditional applications like high-validation math-certified icons for AI alignment aims. This project aims to use Math Agents and mathematical embeddings to address the ageing issue in information systems biology by applying multiscalar physics mathematics to disease models and genomic data. Generative AI with episodic memory could help analyse causal relations in longitudinal health records, using SIR Precision Health models. Genomic data is suggested for addressing the unsolved Alzheimer's disease problem.

How do humans learn language, and can the first language be learned at all? These fundamental questions are still hotly debated. In contemporary linguistics, there are two major schools of thought that give completely opposite answers. According to Chomsky's theory of universal grammar, language cannot be learned because children are not exposed to sufficient data in their linguistic environment. In contrast, usage-based models of language assume a profound relationship between language structure and language use. In particular, contextual mental processing and mental representations are assumed to have the cognitive capacity to capture the complexity of actual language use at all levels. The prime example is syntax, i.e., the rules by which words are assembled into larger units such as sentences. Typically, syntactic rules are expressed as sequences of word classes. However, it remains unclear whether word classes are innate, as implied by universal grammar, or whether they emerge during language acquisition, as suggested by usage-based approaches. Here, we address this issue from a machine learning and natural language processing perspective. In particular, we trained an artificial deep neural network on predicting the next word, provided sequences of consecutive words as input. Subsequently, we analyzed the emerging activation patterns in the hidden layers of the neural network. Strikingly, we find that the internal representations of nine-word input sequences cluster according to the word class of the tenth word to be predicted as output, even though the neural network did not receive any explicit information about syntactic rules or word classes during training. This surprising result suggests, that also in the human brain, abstract representational categories such as word classes may naturally emerge as a consequence of predictive coding and processing during language acquisition.

Large Language Models (LLMs) have made the ambitious quest for generalist agents significantly far from being a fantasy. A key hurdle for building such general models is the diversity and heterogeneity of tasks and modalities. A promising solution is unification, allowing the support of a myriad of tasks and modalities within one unified framework. While few large models (e.g., Flamingo (Alayrac et al., 2022), trained on massive datasets, can support more than two modalities, current small to mid-scale unified models are still limited to 2 modalities, usually image-text or video-text. The question that we ask is: is it possible to build efficiently a unified model that can support all modalities? To answer this, we propose UnIVAL, a step further towards this ambitious goal. Without relying on fancy datasets sizes or models with billions of parameters, the ~ 0.25B parameter UnIVAL model goes beyond two modalities and unifies text, images, video, and audio into a single model. Our model is efficiently pretrained on many tasks, based on task balancing and multimodal curriculum learning. UnIVAL shows competitive performance to existing state-of-the-art approaches, across image and video-text tasks. The feature representations learned from image and video-text modalities, allows the model to achieve competitive performance when finetuned on audio-text tasks, despite not being pretrained on audio. Thanks to the unified model, we propose a novel study on multimodal model merging via weight interpolation of models trained on different multimodal tasks, showing their benefits in particular for out-of-distribution generalization. Finally, we motivate unification by showing the synergy between tasks. The model weights and code are released here: https://github.com/mshukor/UnIVAL.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.

Large pre-trained language models perform remarkably well on tasks that can be done "in one pass", such as generating realistic text or synthesizing computer programs. However, they struggle with tasks that require unbounded multi-step computation, such as adding integers or executing programs. Surprisingly, we find that these same models are able to perform complex multi-step computations -- even in the few-shot regime -- when asked to perform the operation "step by step", showing the results of intermediate computations. In particular, we train transformers to perform multi-step computations by asking them to emit intermediate computation steps into a "scratchpad". On a series of increasingly complex tasks ranging from long addition to the execution of arbitrary programs, we show that scratchpads dramatically improve the ability of language models to perform multi-step computations.

This paper presents NT-Java-1.1B, an open-source specialized code language model built on StarCoderBase-1.1B, designed for coding tasks in Java programming. NT-Java-1.1B achieves state-of-the-art performance, surpassing its base model and majority of other models of similar size on MultiPL-E Java code benchmark. While there have been studies on extending large, generic pre-trained models to improve proficiency in specific programming languages like Python, similar investigations on small code models for other programming languages are lacking. Large code models require specialized hardware like GPUs for inference, highlighting the need for research into building small code models that can be deployed on developer desktops. This paper addresses this research gap by focusing on the development of a small Java code model, NT-Java-1.1B, and its quantized versions, which performs comparably to open models around 1.1B on MultiPL-E Java code benchmarks, making them ideal for desktop deployment. This paper establishes the foundation for specialized models across languages and sizes for a family of NT Models.

By pretraining on trillions of tokens, an LLM gains the capability of text generation. However, to enhance its utility and reduce potential harm, SFT and alignment are applied sequentially to the pretrained model. Due to the differing nature and objective functions of SFT and alignment, catastrophic forgetting has become a significant issue. To address this, we introduce Unified Fine-Tuning (UFT), which integrates SFT and alignment into a single training stage using the same objective and loss functions through an implicit reward function. Our experimental results demonstrate that UFT outperforms SFT on instruction-tuning data alone. Moreover, when combining instruction-tuning data with alignment data, UFT effectively prevents catastrophic forgetting across these two stages and shows a clear advantage over sequentially applying SFT and alignment. This is evident in the significant improvements observed in the ifeval task for instruction-following and the truthful-qa task for factuality. The proposed general fine-tuning framework UFT establishes an effective and efficient pretraining-UFT paradigm for LLM training.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

Large Language Model (LLM) Agents have demonstrated remarkable capabilities in task automation and intelligent decision-making, driving the widespread adoption of agent development frameworks such as LangChain and AutoGen. However, these frameworks predominantly serve developers with extensive technical expertise - a significant limitation considering that only 0.03 % of the global population possesses the necessary programming skills. This stark accessibility gap raises a fundamental question: Can we enable everyone, regardless of technical background, to build their own LLM agents using natural language alone? To address this challenge, we introduce MetaChain-a Fully-Automated and highly Self-Developing framework that enables users to create and deploy LLM agents through Natural Language Alone. Operating as an autonomous Agent Operating System, MetaChain comprises four key components: i) Agentic System Utilities, ii) LLM-powered Actionable Engine, iii) Self-Managing File System, and iv) Self-Play Agent Customization module. This lightweight yet powerful system enables efficient and dynamic creation and modification of tools, agents, and workflows without coding requirements or manual intervention. Beyond its code-free agent development capabilities, MetaChain also serves as a versatile multi-agent system for General AI Assistants. Comprehensive evaluations on the GAIA benchmark demonstrate MetaChain's effectiveness in generalist multi-agent tasks, surpassing existing state-of-the-art methods. Furthermore, MetaChain's Retrieval-Augmented Generation (RAG)-related capabilities have shown consistently superior performance compared to many alternative LLM-based solutions.

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation. Our survey unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems.

Large Language Models (LLMs) have demonstrated remarkable problem-solving and basic mathematics abilities. However, their efficacy is highly contingent on the formulation of the prompt. This study endeavors to quantify the influence of incorporating "positive thinking" into the system message of the prompt, then compare that to systematic prompt optimization. We assess the performance of 60 combinations of system message snippets, tested with and without Chain of Thought prompting, across three models with parameters ranging from 7 to 70 billion on the GSM8K dataset. Our findings reveal that results do not universally generalize across models. In most instances, the inclusion of "positive thinking" prompts positively affected model performance. Notably, however, Llama2-70B exhibited an exception when not utilizing Chain of Thought, as the optimal system message was found to be none at all. Given the combinatorial complexity, and thus computation time, of experimenting with hand-tuning prompts for large black-box models, we then compared the performance of the best "positive thinking" prompt against the output of systematic prompt optimization. We show that employing an automated prompt optimizer emerges as the most effective method for enhancing performance, even when working with smaller open-source models. Additionally, our findings reveal that the highest-scoring, automatically-optimized prompt exhibits a degree of peculiarity far beyond expectations.

Large language models (LLMs) are becoming increasingly better at a wide range of Natural Language Processing tasks (NLP), such as text generation and understanding. Recently, these models have extended their capabilities to coding tasks, bridging the gap between natural languages (NL) and programming languages (PL). Foundational models such as the Generative Pre-trained Transformer (GPT) and LLaMA series have set strong baseline performances in various NL and PL tasks. Additionally, several models have been fine-tuned specifically for code generation, showing significant improvements in code-related applications. Both foundational and fine-tuned models are increasingly used in education, helping students write, debug, and understand code. We present a comprehensive systematic literature review to examine the impact of LLMs in computer science and computer engineering education. We analyze their effectiveness in enhancing the learning experience, supporting personalized education, and aiding educators in curriculum development. We address five research questions to uncover insights into how LLMs contribute to educational outcomes, identify challenges, and suggest directions for future research.

The rapid advancement of artificial intelligence, particularly with the development of Large Language Models (LLMs) built on the transformer architecture, has redefined the capabilities of natural language processing. These models now exhibit remarkable performance across various language-related tasks, such as text generation, question answering, translation, and summarization, often rivaling human-like comprehension. More intriguingly, LLMs have demonstrated emergent abilities extending beyond their core functions, showing proficiency in tasks like commonsense reasoning, code generation, and arithmetic. This survey paper explores the foundational components, scaling mechanisms, and architectural strategies that drive these capabilities. Emphasizing models like GPT and LLaMA, we analyze the impact of exponential data and computational growth on LLM performance, while also addressing the trade-offs associated with scaling. We also examine LLM applications across sectors, such as healthcare, finance, education, and law, highlighting their adaptability and potential to solve domain-specific challenges. Central to this work are the questions of how LLMs generalize across diverse tasks, exhibit planning, and reasoning abilities, and whether these emergent abilities can be systematically elicited or enhanced. In particular, we provide some insights into the CoT (Chain of Thought) and PoT (Plan of Thought) abilities within LLMs, focusing on how pre-training data influences their emergence. Additionally, we investigate LLM-modulo frameworks that integrate external systems, allowing LLMs to handle complex, dynamic tasks. By analyzing these factors, this paper aims to foster the ongoing discussion on the capabilities and limits of LLMs, promoting their responsible development and application in novel and increasingly complex environments.

The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, these models often struggle with tasks requiring complex reasoning, particularly in mathematical problem-solving, due in part to the scarcity of large-scale, high-quality, domain-specific datasets necessary for training sophisticated reasoning abilities. To address this limitation, we introduce Template-based Data Generation (TDG), a novel approach that leverages LLMs (GPT-4) to automatically generate parameterized meta-templates, which are then used to synthesize a vast array of high-quality problems and solutions. Leveraging TDG, we create TemplateMath Part I: TemplateGSM, a dataset comprising over 7 million synthetically generated grade school math problems--each accompanied by code-based and natural language solutions--with the potential to generate an effectively unlimited number more. This dataset alleviates the scarcity of large-scale mathematical datasets and serves as a valuable resource for pre-training, fine-tuning, and evaluating LLMs in mathematical reasoning. Our method not only enables the generation of virtually infinite data but also elevates data augmentation to a new level by using GPT-4 for meta-template generation, ensuring diverse and high-quality problem structures. The TemplateMath Part I: TemplateGSM dataset is publicly available at https://huggingface.co/datasets/math-ai/TemplateGSM. The code is available at https://github.com/iiis-ai/TemplateMath.

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al., 2017) and the Neural GPU (Kaiser & Sutskever, 2016). We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete. Our study also reveals some minimal sets of elements needed to obtain these completeness results.

Instruction tuning -- tuning large language models on instruction-output pairs -- is a promising technique for making models better adapted to the real world. Yet, the key factors driving the model's capability to understand and follow instructions not seen during training remain under-explored. Our investigation begins with a series of synthetic experiments within the theoretical framework of a Turing-complete algorithm called Markov algorithm, which allows fine-grained control over the instruction-tuning data. Generalization and robustness with respect to the training distribution emerge once a diverse enough set of tasks is provided, even though very few examples are provided for each task. We extend these initial results to a real-world application scenario of code generation and find that a more diverse instruction set, extending beyond code-related tasks, improves the performance of code generation. Our observations suggest that a more diverse semantic space for instruction-tuning sets greatly improves the model's ability to follow instructions and perform tasks.

Retrieval-based language models (R-LM) model the probability of natural language text by combining a standard language model (LM) with examples retrieved from an external datastore at test time. While effective, a major bottleneck of using these models in practice is the computationally costly datastore search, which can be performed as frequently as every time step. In this paper, we present RetoMaton - retrieval automaton - which approximates the datastore search, based on (1) saving pointers between consecutive datastore entries, and (2) clustering of entries into "states". This effectively results in a weighted finite automaton built on top of the datastore, instead of representing the datastore as a flat list. The creation of the automaton is unsupervised, and a RetoMaton can be constructed from any text collection: either the original training corpus or from another domain. Traversing this automaton at inference time, in parallel to the LM inference, reduces its perplexity by up to 1.85, or alternatively saves up to 83% of the nearest neighbor searches over kNN-LM (Khandelwal et al., 2020) without hurting perplexity. Our code and trained models are available at https://github.com/neulab/retomaton .

Recent work has shown the immense potential of synthetically generated datasets for training large language models (LLMs), especially for acquiring targeted skills. Current large-scale math instruction tuning datasets such as MetaMathQA (Yu et al., 2024) and MAmmoTH (Yue et al., 2024) are constructed using outputs from closed-source LLMs with commercially restrictive licenses. A key reason limiting the use of open-source LLMs in these data generation pipelines has been the wide gap between the mathematical skills of the best closed-source LLMs, such as GPT-4, and the best open-source LLMs. Building on the recent progress in open-source LLMs, our proposed prompting novelty, and some brute-force scaling, we construct OpenMathInstruct-1, a math instruction tuning dataset with 1.8M problem-solution pairs. The dataset is constructed by synthesizing code-interpreter solutions for GSM8K and MATH, two popular math reasoning benchmarks, using the recently released and permissively licensed Mixtral model. Our best model, OpenMath-CodeLlama-70B, trained on a subset of OpenMathInstruct-1, achieves a score of 84.6% on GSM8K and 50.7% on MATH, which is competitive with the best gpt-distilled models. We release our code, models, and the OpenMathInstruct-1 dataset under a commercially permissive license.

In recent years, large language models (LLMs) have achieved state-of-the-art results in various biological sequence analysis tasks, such as sequence classification, structure prediction, and function prediction. Similar to advancements in AI for other scientific fields, deeper research into biological LLMs has begun to focus on using these models to rediscover important existing biological laws or uncover entirely new patterns in biological sequences.This study leverages GPT-like LLMs to utilize language transfer capabilities to rediscover the genetic code rules of the central dogma. In our experimental design, we transformed the central dogma into a binary classification problem of aligning DNA sequences with protein sequences, where positive examples are matching DNA and protein sequences, and negative examples are non-matching pairs.We first trained a GPT-2 model from scratch using a dataset comprising protein sequences, DNA sequences, and sequences from languages such as English and Chinese. Subsequently, we fine-tuned the model using the English similarity judgment dataset from PAWS-X. When tested on a dataset for DNA and protein sequence alignment judgment, the fine-tuned model achieved a classification accuracy of 76%. The study also analyzed factors contributing to this zero-shot capability, including model training stability and types of training data.This research demonstrates that LLMs can, through the transfer of natural language capabilities and solely relying on the analysis of sequences themselves, rediscover the central dogma without prior knowledge of it. This study opens a new door for AI-driven biological research.

We present a paper abstract writing system based on an attentive neural sequence-to-sequence model that can take a title as input and automatically generate an abstract. We design a novel Writing-editing Network that can attend to both the title and the previously generated abstract drafts and then iteratively revise and polish the abstract. With two series of Turing tests, where the human judges are asked to distinguish the system-generated abstracts from human-written ones, our system passes Turing tests by junior domain experts at a rate up to 30% and by non-expert at a rate up to 80%.

Large language models (LLMs) have recently achieved human-level performance on a range of professional and academic benchmarks. The accessibility of these models has lagged behind their performance. State-of-the-art LLMs require costly infrastructure; are only accessible via rate-limited, geo-locked, and censored web interfaces; and lack publicly available code and technical reports. In this paper, we tell the story of GPT4All, a popular open source repository that aims to democratize access to LLMs. We outline the technical details of the original GPT4All model family, as well as the evolution of the GPT4All project from a single model into a fully fledged open source ecosystem. It is our hope that this paper acts as both a technical overview of the original GPT4All models as well as a case study on the subsequent growth of the GPT4All open source ecosystem.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

We evaluated 3 systems (ELIZA, GPT-3.5 and GPT-4) in a randomized, controlled, and preregistered Turing test. Human participants had a 5 minute conversation with either a human or an AI, and judged whether or not they thought their interlocutor was human. GPT-4 was judged to be a human 54% of the time, outperforming ELIZA (22%) but lagging behind actual humans (67%). The results provide the first robust empirical demonstration that any artificial system passes an interactive 2-player Turing test. The results have implications for debates around machine intelligence and, more urgently, suggest that deception by current AI systems may go undetected. Analysis of participants' strategies and reasoning suggests that stylistic and socio-emotional factors play a larger role in passing the Turing test than traditional notions of intelligence.

Previous studies have typically assumed that large language models are unable to accurately perform arithmetic operations, particularly multiplication of >8 digits, and operations involving decimals and fractions, without the use of calculator tools. This paper aims to challenge this misconception. With sufficient training data, a 2 billion-parameter language model can accurately perform multi-digit arithmetic operations with almost 100% accuracy without data leakage, significantly surpassing GPT-4 (whose multi-digit multiplication accuracy is only 4.3%). We also demonstrate that our MathGLM, fine-tuned from GLM-10B on a dataset with additional multi-step arithmetic operations and math problems described in text, achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set.

Large Language Models (LLMs) represent a significant stride toward Artificial General Intelligence. As scaling laws underscore the potential of increasing model sizes, the academic community has intensified its investigations into LLMs with capacities exceeding 50 billion parameters. This technical report builds on our prior work with Tele-FLM (also known as FLM-2), a publicly available 52-billion-parameter model. We delve into two primary areas: we first discuss our observation of Supervised Fine-tuning (SFT) on Tele-FLM-52B, which supports the "less is more" approach for SFT data construction; second, we demonstrate our experiments and analyses on the best practices for progressively growing a model from 52 billion to 102 billion, and subsequently to 1 trillion parameters. We will open-source a 1T model checkpoint, namely Tele-FLM-1T, to advance further training and research.

Although pre-trained language models~(PLMs) have recently advanced the research progress in mathematical reasoning, they are not specially designed as a capable multi-task solver, suffering from high cost for multi-task deployment (\eg a model copy for a task) and inferior performance on complex mathematical problems in practical applications. To address these issues, in this paper, we propose JiuZhang~2.0, a unified Chinese PLM specially for multi-task mathematical problem solving. Our idea is to maintain a moderate-sized model and employ the cross-task knowledge sharing to improve the model capacity in a multi-task setting. Specially, we construct a Mixture-of-Experts~(MoE) architecture for modeling mathematical text, so as to capture the common mathematical knowledge across tasks. For optimizing the MoE architecture, we design multi-task continual pre-training and multi-task fine-tuning strategies for multi-task adaptation. These training strategies can effectively decompose the knowledge from the task data and establish the cross-task sharing via expert networks. In order to further improve the general capacity of solving different complex tasks, we leverage large language models~(LLMs) as complementary models to iteratively refine the generated solution by our PLM, via in-context learning. Extensive experiments have demonstrated the effectiveness of our model.

Large language models (LLMs) have shown great potential to solve varieties of natural language processing (NLP) tasks, including mathematical reasoning. In this work, we present SkyMath, a large language model for mathematics with 13 billion parameters. By applying self-compare fine-tuning, we have enhanced mathematical reasoning abilities of Skywork-13B-Base remarkably. On GSM8K, SkyMath outperforms all known open-source models of similar size and has established a new SOTA performance.

This paper presents Safurai-001, a new Large Language Model (LLM) with significant potential in the domain of coding assistance. Driven by recent advancements in coding LLMs, Safurai-001 competes in performance with the latest models like WizardCoder [Xu et al., 2023], PanguCoder [Shen et al., 2023] and Phi-1 [Gunasekar et al., 2023] but aims to deliver a more conversational interaction. By capitalizing on the progress in data engineering (including latest techniques of data transformation and prompt engineering) and instruction tuning, this new model promises to stand toe-to-toe with recent closed and open source developments. Recognizing the need for an efficacious evaluation metric for coding LLMs, this paper also introduces GPT4-based MultiParameters, an evaluation benchmark that harnesses varied parameters to present a comprehensive insight into the models functioning and performance. Our assessment shows that Safurai-001 can outperform GPT-3.5 by 1.58% and WizardCoder by 18.78% in the Code Readability parameter and more.

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent limitations in computational depth, rendering them theoretically incapable of solving many reasoning tasks that demand increasingly deep computations. Chain of Thought (CoT) prompting has emerged as a technique to address these architectural limitations, as evidenced by several theoretical studies. It offers a promising approach to solving complex reasoning tasks that were previously beyond the capabilities of these models. Despite its successes, CoT and its variants (such as Tree of Thought, Graph of Thought, etc.) rely on a "one-prompt-for-all" approach, using a single prompt structure (e.g., "think step by step") for a wide range of tasks -- from counting and sorting to solving mathematical and algorithmic problems. This approach poses significant challenges for models to generate the correct reasoning steps, as the model must navigate through a vast prompt template space to find the appropriate template for each task. In this work, we build upon previous theoretical analyses of CoT to demonstrate how the one-prompt-for-all approach can negatively affect the computability of LLMs. We partition the solution search space into two: the prompt space and the answer space. Our findings show that task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance. Through experiments with state-of-the-art LLMs, we reveal a gap in reasoning performance when supervision is applied versus when it is not.

In this paper, we propose KnowCoder, a Large Language Model (LLM) to conduct Universal Information Extraction (UIE) via code generation. KnowCoder aims to develop a kind of unified schema representation that LLMs can easily understand and an effective learning framework that encourages LLMs to follow schemas and extract structured knowledge accurately. To achieve these, KnowCoder introduces a code-style schema representation method to uniformly transform different schemas into Python classes, with which complex schema information, such as constraints among tasks in UIE, can be captured in an LLM-friendly manner. We further construct a code-style schema library covering over 30,000 types of knowledge, which is the largest one for UIE, to the best of our knowledge. To ease the learning process of LLMs, KnowCoder contains a two-phase learning framework that enhances its schema understanding ability via code pretraining and its schema following ability via instruction tuning. After code pretraining on around 1.5B automatically constructed data, KnowCoder already attains remarkable generalization ability and achieves relative improvements by 49.8% F1, compared to LLaMA2, under the few-shot setting. After instruction tuning, KnowCoder further exhibits strong generalization ability on unseen schemas and achieves up to 12.5% and 21.9%, compared to sota baselines, under the zero-shot setting and the low resource setting, respectively. Additionally, based on our unified schema representations, various human-annotated datasets can simultaneously be utilized to refine KnowCoder, which achieves significant improvements up to 7.5% under the supervised setting.

This research introduces a novel evaluation framework designed to assess large language models' (LLMs) ability to acknowledge uncertainty on 675 fundamentally unsolvable problems. Using a curated dataset of graduate-level grand challenge questions with intentionally unknowable answers, we evaluated twelve state-of-the-art LLMs, including both open and closed-source models, on their propensity to admit ignorance rather than generate plausible but incorrect responses. The best models scored in 62-68% accuracy ranges for admitting the problem solution was unknown in fields ranging from biology to philosophy and mathematics. We observed an inverse relationship between problem difficulty and model accuracy, with GPT-4 demonstrating higher rates of uncertainty acknowledgment on more challenging problems (35.8%) compared to simpler ones (20.0%). This pattern indicates that models may be more prone to generate speculative answers when problems appear more tractable. The study also revealed significant variations across problem categories, with models showing difficulty in acknowledging uncertainty in invention and NP-hard problems while performing relatively better on philosophical and psychological challenges. These results contribute to the growing body of research on artificial general intelligence (AGI) assessment by highlighting the importance of uncertainty recognition as a critical component of future machine intelligence evaluation. This impossibility test thus extends previous theoretical frameworks for universal intelligence testing by providing empirical evidence of current limitations in LLMs' ability to recognize their own knowledge boundaries, suggesting new directions for improving model training architectures and evaluation approaches.

Prompt tuning, which only tunes continuous prompts with a frozen language model, substantially reduces per-task storage and memory usage at training. However, in the context of NLU, prior work reveals that prompt tuning does not perform well for normal-sized pretrained models. We also find that existing methods of prompt tuning cannot handle hard sequence labeling tasks, indicating a lack of universality. We present a novel empirical finding that properly optimized prompt tuning can be universally effective across a wide range of model scales and NLU tasks. It matches the performance of finetuning while having only 0.1%-3% tuned parameters. Our method P-Tuning v2 is an implementation of Deep Prompt Tuning li2021prefix,qin2021learning optimized and adapted for NLU. Given the universality and simplicity of P-Tuning v2, we believe it can serve as an alternative to finetuning and a strong baseline for future research.Our code and data are released at https://github.com/THUDM/P-tuning-v2.

Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LMMs to change how mathematicians work.

The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an evolutionary search method, which samples multiple candidate solutions from a large space and evaluates the quality of each candidate through a long training process. As a result, the search tends to be slow. In this paper, we show that large efficiency gains can be obtained by employing a fast unified functional hash, especially through the functional equivalence caching technique, which we also present. The central idea is to detect by hashing when the search method produces equivalent candidates, which occurs very frequently, and this way avoid their costly re-evaluation. Our hash is "functional" in that it identifies equivalent candidates even if they were represented or coded differently, and it is "unified" in that the same algorithm can hash arbitrary representations; e.g. compute graphs, imperative code, or lambda functions. As evidence, we show dramatic improvements on multiple AutoML domains, including neural architecture search and algorithm discovery. Finally, we consider the effect of hash collisions, evaluation noise, and search distribution through empirical analysis. Altogether, we hope this paper may serve as a guide to hashing techniques in AutoML.

The abilities to perceive, learn, and use generalities, similarities, classes, i.e., semantic memory (SM), is central to cognition. Machine learning (ML), neural network, and AI research has been primarily driven by tasks requiring such abilities. However, another central facet of cognition, single-trial formation of permanent memories of experiences, i.e., episodic memory (EM), has had relatively little focus. Only recently has EM-like functionality been added to Deep Learning (DL) models, e.g., Neural Turing Machine, Memory Networks. However, in these cases: a) EM is implemented as a separate module, which entails substantial data movement (and so, time and power) between the DL net itself and EM; and b) individual items are stored localistically within the EM, precluding realizing the exponential representational efficiency of distributed over localist coding. We describe Sparsey, an unsupervised, hierarchical, spatial/spatiotemporal associative memory model differing fundamentally from mainstream ML models, most crucially, in its use of sparse distributed representations (SDRs), or, cell assemblies, which admits an extremely efficient, single-trial learning algorithm that maps input similarity into code space similarity (measured as intersection). SDRs of individual inputs are stored in superposition and because similarity is preserved, the patterns of intersections over the assigned codes reflect the similarity, i.e., statistical, structure, of all orders, not simply pairwise, over the inputs. Thus, SM, i.e., a generative model, is built as a computationally free side effect of the act of storing episodic memory traces of individual inputs, either spatial patterns or sequences. We report initial results on MNIST and on the Weizmann video event recognition benchmarks. While we have not yet attained SOTA class accuracy, learning takes only minutes on a single CPU.

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks, their formal expressiveness and length generalization properties remain underexplored. In this work, we provide insight into the workings of selective SSMs by analyzing their expressiveness and length generalization performance on regular language tasks, i.e., finite-state automaton (FSA) emulation. We address certain limitations of modern SSM-based architectures by introducing the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization on a set of various regular language tasks using a single layer. It utilizes a dictionary of dense transition matrices, a softmax selection mechanism that creates a convex combination of dictionary matrices at each time step, and a readout consisting of layer normalization followed by a linear map. We then proceed to evaluate variants of diagonal selective SSMs by considering their empirical performance on commutative and non-commutative automata. We explain the experimental results with theoretical considerations. Our code is available at https://github.com/IBM/selective-dense-state-space-model.

Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely resembling benchmark questions leaks into the training data, instead of true reasoning ability. To investigate this claim rigorously, we commission Grade School Math 1000 (GSM1k). GSM1k is designed to mirror the style and complexity of the established GSM8k benchmark, the gold standard for measuring elementary mathematical reasoning. We ensure that the two benchmarks are comparable across important metrics such as human solve rates, number of steps in solution, answer magnitude, and more. When evaluating leading open- and closed-source LLMs on GSM1k, we observe accuracy drops of up to 13%, with several families of models (e.g., Phi and Mistral) showing evidence of systematic overfitting across almost all model sizes. At the same time, many models, especially those on the frontier, (e.g., Gemini/GPT/Claude) show minimal signs of overfitting. Further analysis suggests a positive relationship (Spearman's r^2=0.32) between a model's probability of generating an example from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that many models may have partially memorized GSM8k.

Large language models (LLMs) are a new and powerful tool for a wide span of applications involving natural language and demonstrate impressive code generation abilities. In this paper, we explore the capabilitity of state-of-the-art LLMs, including closed-source options like OpenAI GPT-4 and open-source alternatives like Meta AI Codellama, to automatically generate tests and use these tests to validate and verify compiler implementations of a directive-based programming paradigm, OpenACC. Our approach entails exploring various prompt engineering techniques including a code template, retrieval-augmented generation (RAG) with code template, expressive prompt using RAG with code template, one-shot example, and RAG with one-shot example. This paper focusses on (a) exploring the capabilities of the latest LLMs for code generation, (b) investigating prompt and fine tuning methods, and (c) analyzing the outcome of LLMs generated tests

Upon its release in late 2022, ChatGPT has brought a seismic shift in the entire landscape of AI, both in research and commerce. Through instruction-tuning a large language model (LLM) with supervised fine-tuning and reinforcement learning from human feedback, it showed that a model could answer human questions and follow instructions on a broad panel of tasks. Following this success, interests in LLMs have intensified, with new LLMs flourishing at frequent interval across academia and industry, including many start-ups focused on LLMs. While closed-source LLMs (e.g., OpenAI's GPT, Anthropic's Claude) generally outperform their open-source counterparts, the progress on the latter has been rapid with claims of achieving parity or even better on certain tasks. This has crucial implications not only on research but also on business. In this work, on the first anniversary of ChatGPT, we provide an exhaustive overview of this success, surveying all tasks where an open-source LLM has claimed to be on par or better than ChatGPT.

Computer Science (CS) stands as a testament to the intricacies of human intelligence, profoundly advancing the development of artificial intelligence and modern society. However, the current community of large language models (LLMs) overly focuses on benchmarks for analyzing specific foundational skills (e.g. mathematics and code generation), neglecting an all-round evaluation of the computer science field. To bridge this gap, we introduce CS-Bench, the first bilingual (Chinese-English) benchmark dedicated to evaluating the performance of LLMs in computer science. CS-Bench comprises approximately 5K meticulously curated test samples, covering 26 subfields across 4 key areas of computer science, encompassing various task forms and divisions of knowledge and reasoning. Utilizing CS-Bench, we conduct a comprehensive evaluation of over 30 mainstream LLMs, revealing the relationship between CS performance and model scales. We also quantitatively analyze the reasons for failures in existing LLMs and highlight directions for improvements, including knowledge supplementation and CS-specific reasoning. Further cross-capability experiments show a high correlation between LLMs' capabilities in computer science and their abilities in mathematics and coding. Moreover, expert LLMs specialized in mathematics and coding also demonstrate strong performances in several CS subfields. Looking ahead, we envision CS-Bench serving as a cornerstone for LLM applications in the CS field and paving new avenues in assessing LLMs' diverse reasoning capabilities. The CS-Bench data and evaluation code are available at https://github.com/csbench/csbench.

Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a transformer's classification decisions become less and less confident (that is, with cross-entropy approaching 1 bit per string) as input strings get longer and longer. We examine this limitation using two languages: PARITY, the language of bit strings with an odd number of 1s, and FIRST, the language of bit strings starting with a 1. We demonstrate three ways of overcoming the limitation suggested by Hahn's lemma. First, we settle an open question by constructing a transformer that recognizes PARITY with perfect accuracy, and similarly for FIRST. Second, we use layer normalization to bring the cross-entropy of both models arbitrarily close to zero. Third, when transformers need to focus on a single position, as for FIRST, we find that they can fail to generalize to longer strings; we offer a simple remedy to this problem that also improves length generalization in machine translation.

A proper code evaluation metric (CEM) profoundly impacts the evolution of code generation, which is an important research field in NLP and software engineering. Prevailing match-based CEMs (e.g., BLEU, Accuracy, and CodeBLEU) suffer from two significant drawbacks. 1. They primarily measure the surface differences between codes without considering their functional equivalence. However, functional equivalence is pivotal in evaluating the effectiveness of code generation, as different codes can perform identical operations. 2. They are predominantly designed for the Ref-only input format. However, code evaluation necessitates versatility in input formats. Aside from Ref-only, there are NL-only and Ref\&NL formats, which existing match-based CEMs cannot effectively accommodate. In this paper, we propose CodeScore, a large language model (LLM)-based CEM, which estimates the functional correctness of generated code on three input types. To acquire CodeScore, we present UniCE, a unified code generation learning framework, for LLMs to learn code execution (i.e., learning PassRatio and Executability of generated code) with unified input. Extensive experimental results on multiple code evaluation datasets demonstrate that CodeScore absolutely improves up to 58.87% correlation with functional correctness compared to other CEMs, achieves state-of-the-art performance, and effectively handles three input formats.

We introduce a new type of test, called a Turing Experiment (TE), for evaluating how well a language model, such as GPT-3, can simulate different aspects of human behavior. Unlike the Turing Test, which involves simulating a single arbitrary individual, a TE requires simulating a representative sample of participants in human subject research. We give TEs that attempt to replicate well-established findings in prior studies. We design a methodology for simulating TEs and illustrate its use to compare how well different language models are able to reproduce classic economic, psycholinguistic, and social psychology experiments: Ultimatum Game, Garden Path Sentences, Milgram Shock Experiment, and Wisdom of Crowds. In the first three TEs, the existing findings were replicated using recent models, while the last TE reveals a "hyper-accuracy distortion" present in some language models.

Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the expressivity of LLMs with CoT in solving fundamental mathematical and decision-making problems. By using circuit complexity theory, we first give impossibility results showing that bounded-depth Transformers are unable to directly produce correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of constant size suffice to solve both tasks by generating CoT derivations using a commonly used math language format. Moreover, we show LLMs with CoT can handle a general class of decision-making problems known as Dynamic Programming, thus justifying its power in tackling complex real-world tasks. Finally, an extensive set of experiments show that, while Transformers always fail to directly predict the answers, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.

Enabling Large Language Models (LLMs) to handle a wider range of complex tasks (e.g., coding, math) has drawn great attention from many researchers. As LLMs continue to evolve, merely increasing the number of model parameters yields diminishing performance improvements and heavy computational costs. Recently, OpenAI's o1 model has shown that inference strategies (i.e., Test-time Compute methods) can also significantly enhance the reasoning capabilities of LLMs. However, the mechanisms behind these methods are still unexplored. In our work, to investigate the reasoning patterns of o1, we compare o1 with existing Test-time Compute methods (BoN, Step-wise BoN, Agent Workflow, and Self-Refine) by using OpenAI's GPT-4o as a backbone on general reasoning benchmarks in three domains (i.e., math, coding, commonsense reasoning). Specifically, first, our experiments show that the o1 model has achieved the best performance on most datasets. Second, as for the methods of searching diverse responses (e.g., BoN), we find the reward models' capability and the search space both limit the upper boundary of these methods. Third, as for the methods that break the problem into many sub-problems, the Agent Workflow has achieved better performance than Step-wise BoN due to the domain-specific system prompt for planning better reasoning processes. Fourth, it is worth mentioning that we have summarized six reasoning patterns of o1, and provided a detailed analysis on several reasoning benchmarks.

The recent success of Large Language Models (LLMs) signifies an impressive stride towards artificial general intelligence. They have shown a promising prospect in automatically completing tasks upon user instructions, functioning as brain-like coordinators. The associated risks will be revealed as we delegate an increasing number of tasks to machines for automated completion. A big question emerges: how can we make machines behave responsibly when helping humans automate tasks as personal copilots? In this paper, we explore this question in depth from the perspectives of feasibility, completeness and security. In specific, we present Responsible Task Automation (ResponsibleTA) as a fundamental framework to facilitate responsible collaboration between LLM-based coordinators and executors for task automation with three empowered capabilities: 1) predicting the feasibility of the commands for executors; 2) verifying the completeness of executors; 3) enhancing the security (e.g., the protection of users' privacy). We further propose and compare two paradigms for implementing the first two capabilities. One is to leverage the generic knowledge of LLMs themselves via prompt engineering while the other is to adopt domain-specific learnable models. Moreover, we introduce a local memory mechanism for achieving the third capability. We evaluate our proposed ResponsibleTA on UI task automation and hope it could bring more attentions to ensuring LLMs more responsible in diverse scenarios. The research project homepage is at https://task-automation-research.github.io/responsible_task_automation.

In this paper, we present Jellyfish, an open-source LLM as a universal task solver for DP. Built on the Llama 2 13B model, Jellyfish is instruction-tuned with the datasets of several typical DP tasks including error detection, data imputation, schema matching, and entity matching, and delivers generalizability to other tasks. Remarkably, Jellyfish can operate on a local, single, and low-priced GPU with its 13 billion parameters, ensuring data security and enabling further tuning. Its proficiency in understanding natural language allows users to manually craft instructions for DP tasks. Unlike many existing methods that heavily rely on prior knowledge, Jellyfish acquires domain knowledge during its tuning process and integrates optional knowledge injection during inference. A distinctive feature of Jellyfish is its interpreter, which elucidates its output decisions. To construct Jellyfish, we develop a series of pre-tuning and DP-tuning techniques. Jellyfish is equipped with an instance serializer, which automatically translates raw data into model prompts, and a knowledge injector, which optionally introduces task- and dataset-specific knowledge to enhance DP performance. Our evaluation of Jellyfish, using a range of real datasets, shows its competitiveness compared to state-of-the-art methods and its strong generalizability to unseen tasks. Jellyfish's performance rivals that of GPT series models, and its interpreter offers enhanced reasoning capabilities compared to GPT-3.5. Furthermore, our evaluation highlights the effectiveness of the techniques employed in constructing Jellyfish. Our model is available at Hugging Face: https://huggingface.co/NECOUDBFM/Jellyfish .

We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original mathematical terms -- might be addressable via generation from language models. We present an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyze its performance. GPT-f found new short proofs that were accepted into the main Metamath library, which is to our knowledge, the first time a deep-learning based system has contributed proofs that were adopted by a formal mathematics community.

Planning remains one of the last standing bastions for large language models (LLMs), which now turn their attention to search. Most of the literature uses the language models as world models to define the search space, forgoing soundness for the sake of flexibility. A recent work, Thought of Search (ToS), proposed defining the search space with code, having the language models produce that code. ToS requires a human in the loop, collaboratively producing a sound successor function and goal test. The result, however, is worth the effort: all the tested datasets were solved with 100% accuracy. At the same time LLMs have demonstrated significant progress in code generation and refinement for complex reasoning tasks. In this work, we automate ToS (AutoToS), completely taking the human out of the loop of solving planning problems. AutoToS guides the language model step by step towards the generation of sound and complete search components, through feedback from both generic and domain specific unit tests. We achieve 100% accuracy, with minimal feedback iterations, using LLMs of various sizes on all evaluated domains.

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study large-scale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NaturalProver, a language model that generates proofs by conditioning on background references (e.g. theorems and definitions that are either retrieved or human-provided), and optionally enforces their presence with constrained decoding. On theorems from the NaturalProofs benchmark, NaturalProver improves the quality of next-step suggestions and generated proofs over fine-tuned GPT-3, according to human evaluations from university-level mathematics students. NaturalProver is capable of proving some theorems that require short (2-6 step) proofs, and providing next-step suggestions that are rated as correct and useful over 40% of the time, which is to our knowledge the first demonstration of these capabilities using neural language models.

We report a flexible language-model based deep learning strategy, applied here to solve complex forward and inverse problems in protein modeling, based on an attention neural network that integrates transformer and graph convolutional architectures in a causal multi-headed graph mechanism, to realize a generative pretrained model. The model is applied to predict secondary structure content (per-residue level and overall content), protein solubility, and sequencing tasks. Further trained on inverse tasks, the model is rendered capable of designing proteins with these properties as target features. The model is formulated as a general framework, completely prompt-based, and can be adapted for a variety of downstream tasks. We find that adding additional tasks yields emergent synergies that the model exploits in improving overall performance, beyond what would be possible by training a model on each dataset alone. Case studies are presented to validate the method, yielding protein designs specifically focused on structural proteins, but also exploring the applicability in the design of soluble, antimicrobial biomaterials. While our model is trained to ultimately perform 8 distinct tasks, with available datasets it can be extended to solve additional problems. In a broader sense, this work illustrates a form of multiscale modeling that relates a set of ultimate building blocks (here, byte-level utf8 characters) to complex output. This materiomic scheme captures complex emergent relationships between universal building block and resulting properties via a synergizing learning capacity to express a set of potentialities embedded in the knowledge used in training, via the interplay of universality and diversity.

Large Language Models (LLMs) have demonstrated remarkable performance in solving math problems, a hallmark of human intelligence. Despite high success rates on current benchmarks; however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70\% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.

Large Language Models (LLMs) represent a revolution in AI. However, they also pose many significant risks, such as the presence of biased, private, copyrighted or harmful text. For this reason we need open, transparent and safe solutions. We introduce a complete open-source ecosystem for developing and testing LLMs. The goal of this project is to boost open alternatives to closed-source approaches. We release h2oGPT, a family of fine-tuned LLMs from 7 to 70 Billion parameters. We also introduce H2O LLM Studio, a framework and no-code GUI designed for efficient fine-tuning, evaluation, and deployment of LLMs using the most recent state-of-the-art techniques. Our code and models are licensed under fully permissive Apache 2.0 licenses. We believe open-source language models help to boost AI development and make it more accessible and trustworthy. The demo is available at: https://gpt.h2o.ai/

Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the Decomposition of thought with code assistance and self-correction for mathematical reasoning, dubbed as DotaMath. DotaMath models tackle complex mathematical tasks by decomposing them into simpler logical subtasks, leveraging code to solve these subtasks, obtaining fine-grained feedback from the code interpreter, and engaging in self-reflection and correction. By annotating diverse interactive tool-use trajectories and employing query evolution on GSM8K and MATH datasets, we generate an instruction fine-tuning dataset called DotaMathQA with 574K query-response pairs. We train a series of base LLMs using imitation learning on DotaMathQA, resulting in DotaMath models that achieve remarkable performance compared to open-source LLMs across various in-domain and out-of-domain benchmarks. Notably, DotaMath-deepseek-7B showcases an outstanding performance of 64.8% on the competitive MATH dataset and 86.7% on GSM8K. Besides, DotaMath-deepseek-7B maintains strong competitiveness on a series of in-domain and out-of-domain benchmarks (Avg. 80.1%). Looking forward, we anticipate that the DotaMath paradigm will open new pathways for addressing intricate mathematical problems. Our code is publicly available at https://github.com/ChengpengLi1003/DotaMath.

Since the release of T\"ULU [Wang et al., 2023b], open resources for instruction tuning have developed quickly, from better base models to new finetuning techniques. We test and incorporate a number of these advances into T\"ULU, resulting in T\"ULU 2, a suite of improved T\"ULU models for advancing the understanding and best practices of adapting pretrained language models to downstream tasks and user preferences. Concretely, we release: (1) T\"ULU-V2-mix, an improved collection of high-quality instruction datasets; (2) T\"ULU 2, LLAMA-2 models finetuned on the V2 mixture; (3) T\"ULU 2+DPO, T\"ULU 2 models trained with direct preference optimization (DPO), including the largest DPO-trained model to date (T\"ULU 2+DPO 70B); (4) CODE T\"ULU 2, CODE LLAMA models finetuned on our V2 mix that outperform CODE LLAMA and its instruction-tuned variant, CODE LLAMA-Instruct. Our evaluation from multiple perspectives shows that the T\"ULU 2 suite achieves state-of-the-art performance among open models and matches or exceeds the performance of GPT-3.5-turbo-0301 on several benchmarks. We release all the checkpoints, data, training and evaluation code to facilitate future open efforts on adapting large language models.

Large language models are redefining software engineering by implementing AI-powered techniques throughout the whole software development process, including requirement gathering, software architecture, code generation, testing, and deployment. However, it is still difficult to develop a cohesive platform that consistently produces the best outcomes across all stages. The objective of this study is to develop a unified platform that utilizes multiple artificial intelligence agents to automate the process of transforming user requirements into well-organized deliverables. These deliverables include user stories, prioritization, and UML sequence diagrams, along with the modular approach to APIs, unit tests, and end-to-end tests. Additionally, the platform will organize tasks, perform security and compliance, and suggest design patterns and improvements for non-functional requirements. We allow users to control and manage each phase according to their preferences. In addition, the platform provides security and compliance checks following European standards and proposes design optimizations. We use multiple models, such as GPT-3.5, GPT-4, and Llama3 to enable to generation of modular code as per user choice. The research also highlights the limitations and future research discussions to overall improve the software development life cycle. The source code for our uniform platform is hosted on GitHub, enabling additional experimentation and supporting both research and practical uses. \end

Large Language Models (LLMs) have demonstrated great potential in various language processing tasks, and recent studies have explored their application in compiler optimizations. However, all these studies focus on the conventional open-source LLMs, such as Llama2, which lack enhanced reasoning mechanisms. In this study, we investigate the errors produced by the fine-tuned 7B-parameter Llama2 model as it attempts to learn and apply a simple peephole optimization for the AArch64 assembly code. We provide an analysis of the errors produced by the LLM and compare it with state-of-the-art OpenAI models which implement advanced reasoning logic, including GPT-4o and GPT-o1 (preview). We demonstrate that OpenAI GPT-o1, despite not being fine-tuned, outperforms the fine-tuned Llama2 and GPT-4o. Our findings indicate that this advantage is largely due to the chain-of-thought reasoning implemented in GPT-o1. We hope our work will inspire further research on using LLMs with enhanced reasoning mechanisms and chain-of-thought for code generation and optimization.

Instructing the model to generate a sequence of intermediate steps, a.k.a., a chain of thought (CoT), is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. However, the mechanism behind CoT remains unclear. This work provides a theoretical understanding of the power of CoT for decoder-only transformers through the lens of expressiveness. Conceptually, CoT empowers the model with the ability to perform inherently serial computation, which is otherwise lacking in transformers, especially when depth is low. Given input length n, previous works have shown that constant-depth transformers with finite precision poly(n) embedding size can only solve problems in TC^0 without CoT. We first show an even tighter expressiveness upper bound for constant-depth transformers with constant-bit precision, which can only solve problems in AC^0, a proper subset of TC^0. However, with T steps of CoT, constant-depth transformers using constant-bit precision and O(log n) embedding size can solve any problem solvable by boolean circuits of size T. Empirically, enabling CoT dramatically improves the accuracy for tasks that are hard for parallel computation, including the composition of permutation groups, iterated squaring, and circuit value problems, especially for low-depth transformers.

To improve language models' proficiency in mathematical reasoning via continual pretraining, we introduce a novel strategy that leverages base language models for autonomous data selection. Departing from conventional supervised fine-tuning or trained classifiers with human-annotated data, our approach utilizes meta-prompted language models as zero-shot verifiers to autonomously evaluate and select high-quality mathematical content, and we release the curated open-source AutoMathText dataset encompassing over 200GB of data. To demonstrate the efficacy of our method, we continuously pretrained a 7B-parameter Mistral language model on the AutoMathText dataset, achieving substantial improvements in downstream performance on the MATH dataset with a token amount reduced by orders of magnitude compared to previous continuous pretraining works. Our method showcases a 2 times increase in pretraining token efficiency compared to baselines, underscoring the potential of our approach in enhancing models' mathematical reasoning capabilities. The AutoMathText dataset is available at https://huggingface.co/datasets/math-ai/AutoMathText. The code is available at https://github.com/yifanzhang-pro/AutoMathText.

As language models scale up, it becomes increasingly expensive to verify research ideas because conclusions on small models do not trivially transfer to large ones. A possible solution is to establish a generic system that directly predicts some metrics for large models solely based on the results and hyperparameters from small models. Existing methods based on scaling laws require hyperparameter search on the largest models, which is impractical with limited resources. We address this issue by presenting our discoveries indicating that Maximal Update parametrization (Mup) enables accurate fitting of scaling laws for hyperparameters close to common loss basins, without any search. Thus, different models can be directly compared on large scales with loss prediction even before the training starts. We propose a new paradigm as a first step towards reliable academic research for any model scale without heavy computation. Code is publicly available at https://github.com/cofe-ai/Mu-scaling.

Recently, Language Models (LMs) instruction-tuned on multiple tasks, also known as multitask-prompted fine-tuning (MT), have shown the capability to generalize to unseen tasks. Previous work has shown that scaling the number of training tasks is the key component in making stronger MT LMs. In this work, we report an unexpected finding that an expert LM fine-tuned on just a single task can outperform an MT LM trained with 300+ different tasks on 11 different unseen datasets and on 13 datasets of the BIG-bench benchmark by a mean accuracy of 3.20% and 1.29%, respectively. This finding casts doubt on the previously held belief that simply scaling the number of tasks makes stronger MT LMs. Leveraging this finding, we further show that this distributed approach of training a separate expert LM per training task instead of a single MT LM for zero-shot inference possesses many benefits including (1) avoiding negative task transfer that often occurs during instruction tuning, (2) being able to continually learn new tasks without having to re-train on previous tasks to avoid catastrophic forgetting, and (3) showing compositional capabilities when merging individual experts together. The code is available at https://github.com/joeljang/ELM.

In this paper, we present Paramanu-Ganita, a 208 million parameter novel Auto Regressive (AR) decoder based language model on mathematics. The model is pretrained from scratch at context size of 4096 on our curated mixed mathematical corpus. We evaluate our model on both perplexity metric and GSM8k mathematical benchmark. Paramanu-Ganita despite being 35 times smaller than 7B LLMs, outperformed generalist LLMs such as LLaMa-1 7B by 28.4% points, LLaMa-2 7B by 27.6% points, Falcon 7B by 32.6% points, PaLM 8B by 35.3% points, and math specialised LLMs such as Minerva 8B by 23.2% points, and LLEMMA-7B by 3.0% points in GSM8k test accuracy metric respectively. Paramanu-Ganita also outperformed giant LLMs like PaLM 62B by 6.4% points, Falcon 40B by 19.8% points, LLaMa-1 33B by 3.8% points and Vicuna 13B by 11.8% points respectively. The large significant margin improvement in performance of our math model over the existing LLMs signifies that reasoning capabilities of language model are just not restricted to LLMs with humongous number of parameters. Paramanu-Ganita took 146 hours of A100 training whereas math specialised LLM, LLEMMA 7B, was trained for 23,000 A100 hours of training equivalent. Thus, our approach of pretraining powerful domain specialised language models from scratch for domain adaptation is much more cost-effective than performing continual training of LLMs for domain adaptation. Hence, we conclude that for strong mathematical reasoning abilities of language model, we do not need giant LLMs and immense computing power to our end. In the end, we want to point out that we have only trained Paramanu-Ganita only on a part of our entire mathematical corpus and yet to explore the full potential of our model.

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, and advanced CoT methodologies. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is positioned as a valuable resource, poised to facilitate and inspire future innovation among researchers invested in advancing this domain.

Zero-shot and in-context learning enable solving tasks without model fine-tuning, making them essential for developing generative model solutions. Therefore, it is crucial to understand whether a pretrained model can be prompted to approximate any function, i.e., whether it is a universal in-context approximator. While it was recently shown that transformer models do possess this property, these results rely on their attention mechanism. Hence, these findings do not apply to fully recurrent architectures like RNNs, LSTMs, and the increasingly popular SSMs. We demonstrate that RNNs, LSTMs, GRUs, Linear RNNs, and linear gated architectures such as Mamba and Hawk/Griffin can also serve as universal in-context approximators. To streamline our argument, we introduce a programming language called LSRL that compiles to these fully recurrent architectures. LSRL may be of independent interest for further studies of fully recurrent models, such as constructing interpretability benchmarks. We also study the role of multiplicative gating and observe that architectures incorporating such gating (e.g., LSTMs, GRUs, Hawk/Griffin) can implement certain operations more stably, making them more viable candidates for practical in-context universal approximation.

Large Language Models (LLMs) trained on code are revolutionizing the software development process. Increasingly, code LLMs are being integrated into software development environments to improve the productivity of human programmers, and LLM-based agents are beginning to show promise for handling complex tasks autonomously. Realizing the full potential of code LLMs requires a wide range of capabilities, including code generation, fixing bugs, explaining and documenting code, maintaining repositories, and more. In this work, we introduce the Granite series of decoder-only code models for code generative tasks, trained with code written in 116 programming languages. The Granite Code models family consists of models ranging in size from 3 to 34 billion parameters, suitable for applications ranging from complex application modernization tasks to on-device memory-constrained use cases. Evaluation on a comprehensive set of tasks demonstrates that Granite Code models consistently reaches state-of-the-art performance among available open-source code LLMs. The Granite Code model family was optimized for enterprise software development workflows and performs well across a range of coding tasks (e.g. code generation, fixing and explanation), making it a versatile all around code model. We release all our Granite Code models under an Apache 2.0 license for both research and commercial use.

Large Language Models (LLMs) are advanced Artificial Intelligence (AI) systems that have undergone extensive training using large datasets in order to understand and produce language that closely resembles that of humans. These models have reached a level of proficiency where they are capable of successfully completing university exams across several disciplines and generating functional code to handle novel problems. This research investigates the coding proficiency of ChatGPT 3.5, a LLM released by OpenAI in November 2022, which has gained significant recognition for its impressive text generating and code creation capabilities. The skill of the model in creating code snippets is evaluated across 10 various programming languages and 4 different software domains. Based on the findings derived from this research, major unexpected behaviors and limitations of the model have been identified. This study aims to identify potential areas for development and examine the ramifications of automated code generation on the evolution of programming languages and on the tech industry.

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 13% and 29%. Remarkably, our MAmmoTH-7B model reaches 35% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 25%, and the MAmmoTH-34B model achieves 46% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

We present QuantumLLMInstruct (QLMMI), an innovative dataset featuring over 500,000 meticulously curated instruction-following problem-solution pairs designed specifically for quantum computing - the largest and most comprehensive dataset of its kind. Originating from over 90 primary seed domains and encompassing hundreds of subdomains autonomously generated by LLMs, QLMMI marks a transformative step in the diversity and richness of quantum computing datasets. Designed for instruction fine-tuning, QLMMI seeks to significantly improve LLM performance in addressing complex quantum computing challenges across a wide range of quantum physics topics. While Large Language Models (LLMs) have propelled advancements in computational science with datasets like Omni-MATH and OpenMathInstruct, these primarily target Olympiad-level mathematics, leaving quantum computing largely unexplored. The creation of QLMMI follows a rigorous four-stage methodology. Initially, foundational problems are developed using predefined templates, focusing on critical areas such as synthetic Hamiltonians, QASM code generation, Jordan-Wigner transformations, and Trotter-Suzuki quantum circuit decompositions. Next, detailed and domain-specific solutions are crafted to ensure accuracy and relevance. In the third stage, the dataset is enriched through advanced reasoning techniques, including Chain-of-Thought (CoT) and Task-Oriented Reasoning and Action (ToRA), which enhance problem-solution diversity while adhering to strict mathematical standards. Lastly, a zero-shot Judge LLM performs self-assessments to validate the dataset's quality and reliability, minimizing human oversight requirements.

We investigate the mathematical capabilities of ChatGPT by testing it on publicly available datasets, as well as hand-crafted ones, and measuring its performance against other models trained on a mathematical corpus, such as Minerva. We also test whether ChatGPT can be a useful assistant to professional mathematicians by emulating various use cases that come up in the daily professional activities of mathematicians (question answering, theorem searching). In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, only cover elementary mathematics. We address this issue by introducing a new dataset: GHOSTS. It is the first natural-language dataset made and curated by working researchers in mathematics that (1) aims to cover graduate-level mathematics and (2) provides a holistic overview of the mathematical capabilities of language models. We benchmark ChatGPT on GHOSTS and evaluate performance against fine-grained criteria. We make this new dataset publicly available to assist a community-driven comparison of ChatGPT with (future) large language models in terms of advanced mathematical comprehension. We conclude that contrary to many positive reports in the media (a potential case of selection bias), ChatGPT's mathematical abilities are significantly below those of an average mathematics graduate student. Our results show that ChatGPT often understands the question but fails to provide correct solutions. Hence, if your goal is to use it to pass a university exam, you would be better off copying from your average peer!

Finite state machines (FSMs) are widely used to manage robot behavior logic, particularly in real-world applications that require a high degree of reliability and structure. However, traditional manual FSM design and modification processes can be time-consuming and error-prone. We propose that large language models (LLMs) can assist developers in editing FSM code for real-world robotic use cases. LLMs, with their ability to use context and process natural language, offer a solution for FSM modification with high correctness, allowing developers to update complex control logic through natural language instructions. Our approach leverages few-shot prompting and language-guided code generation to reduce the amount of time it takes to edit an FSM. To validate this approach, we evaluate it on a real-world robotics dataset, demonstrating its effectiveness in practical scenarios.

State of the art sequence-to-sequence models for large scale tasks perform a fixed number of computations for each input sequence regardless of whether it is easy or hard to process. In this paper, we train Transformer models which can make output predictions at different stages of the network and we investigate different ways to predict how much computation is required for a particular sequence. Unlike dynamic computation in Universal Transformers, which applies the same set of layers iteratively, we apply different layers at every step to adjust both the amount of computation as well as the model capacity. On IWSLT German-English translation our approach matches the accuracy of a well tuned baseline Transformer while using less than a quarter of the decoder layers.

Code provides a general syntactic structure to build complex programs and perform precise computations when paired with a code interpreter -- we hypothesize that language models (LMs) can leverage code-writing to improve Chain of Thought reasoning not only for logic and arithmetic tasks, but also for linguistic ones (and in particular, those that are a mix of both). For example, consider prompting an LM to write code that counts the number of times it detects sarcasm in an essay: the LM may struggle to write an implementation for "detect_sarcasm(string)" that can be executed by the interpreter (handling the edge cases would be insurmountable). However, LMs may still produce a valid solution if they are used not only to write the code, but also to selectively "emulate" the interpreter by generating the expected output of "detect_sarcasm(string)" and other lines of code (e.g., that the interpreter could not compile). In this work, we propose Chain of Code (CoT), a simple yet surprisingly effective extension that improves LM code-driven reasoning. The key idea is to encourage LMs to format linguistic sub-tasks in a program as flexible pseudocode that the compiler can explicitly catch undefined behaviors and hand off to simulate with an LM (as an "LMulator"). Experiments demonstrate that Chain of Code outperforms Chain of Thought and other baselines across a variety of benchmarks; on BIG-Bench Hard, Chain of Code achieves 84%, a gain of 12% over Chain of Thought. CoT scales well with large and small models alike, and broadens the scope of reasoning questions that LMs can correctly answer by "thinking in code". Project webpage: https://chain-of-code.github.io/.

While a lot of recent research focuses on enhancing the textual reasoning capabilities of Large Language Models (LLMs) by optimizing the multi-agent framework or reasoning chains, several benchmark tasks can be solved with 100% success through direct coding, which is more scalable and avoids the computational overhead associated with textual iterating and searching. Textual reasoning has inherent limitations in solving tasks with challenges in math, logics, optimization, and searching, which is unlikely to be solved by simply scaling up the model and data size. The recently released OpenAI GPT Code Interpreter and multi-agent frameworks such as AutoGen have demonstrated remarkable proficiency of integrating code generation and execution to solve complex tasks using LLMs. However, based on our experiments on 7 existing popular methods for steering code/text generation in both single- and multi-turn settings with 14 tasks and 6 types of LLMs (including the new O1-preview), currently there is no optimal method to correctly steer LLMs to write code when needed. We discover some interesting patterns on when models use code vs. textual reasoning with the evolution to task complexity and model sizes, which even result in an astonishingly inverse scaling law. We also discover that results from LLM written code are not always better than using textual reasoning, even if the task could be solved through code. To mitigate the above issues, we propose three methods to better steer LLM code/text generation and achieve a notable improvement. The costs of token lengths and runtime are thoroughly discussed for all the methods. We believe the problem of steering LLM code/text generation is critical for future research and has much space for further improvement. Project Page, Datasets, and Codes are available at https://yongchao98.github.io/CodeSteer/.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

Pre-trained on massive amounts of code and text data, large language models (LLMs) have demonstrated remarkable achievements in performing code generation tasks. With additional execution-based feedback, these models can act as agents with capabilities to self-refine and improve generated code autonomously. However, on challenging coding tasks with extremely large search space, current agentic approaches still struggle with multi-stage planning, generating, and debugging. To address this problem, we propose CodeTree, a framework for LLM agents to efficiently explore the search space in different stages of the code generation process. Specifically, we adopted a unified tree structure to explicitly explore different coding strategies, generate corresponding coding solutions, and subsequently refine the solutions. In each stage, critical decision-making (ranking, termination, expanding) of the exploration process is guided by both the environmental execution-based feedback and LLM-agent-generated feedback. We comprehensively evaluated CodeTree on 7 code generation benchmarks and demonstrated the significant performance gains of CodeTree against strong baselines. Using GPT-4o as the base model, we consistently achieved top results of 95.1 on HumanEval, 98.7 on MBPP, and 43.0 on CodeContests. On the challenging SWEBench benchmark, our approach led to significant performance gains.

Existing Large Language Models (LLM) can invoke a variety of tools and APIs to complete complex tasks. The computer, as the most powerful and universal tool, could potentially be controlled directly by a trained LLM agent. Powered by the computer, we can hopefully build a more generalized agent to assist humans in various daily digital works. In this paper, we construct an environment for a Vision Language Model (VLM) agent to interact with a real computer screen. Within this environment, the agent can observe screenshots and manipulate the Graphics User Interface (GUI) by outputting mouse and keyboard actions. We also design an automated control pipeline that includes planning, acting, and reflecting phases, guiding the agent to continuously interact with the environment and complete multi-step tasks. Additionally, we construct the ScreenAgent Dataset, which collects screenshots and action sequences when completing a variety of daily computer tasks. Finally, we trained a model, ScreenAgent, which achieved computer control capabilities comparable to GPT-4V and demonstrated more precise UI positioning capabilities. Our attempts could inspire further research on building a generalist LLM agent. The code is available at https://github.com/niuzaisheng/ScreenAgent.

Fine-tuning on instruction data has been widely validated as an effective practice for implementing chat language models like ChatGPT. Scaling the diversity and quality of such data, although straightforward, stands a great chance of leading to improved performance. This paper aims to improve the upper bound of open-source models further. We first provide a systematically designed, diverse, informative, large-scale dataset of instructional conversations, UltraChat, which does not involve human queries. Our objective is to capture the breadth of interactions that a human might have with an AI assistant and employs a comprehensive framework to generate multi-turn conversation iteratively. UltraChat contains 1.5 million high-quality multi-turn dialogues and covers a wide range of topics and instructions. Our statistical analysis of UltraChat reveals its superiority in various key metrics, including scale, average length, diversity, coherence, etc., solidifying its position as a leading open-source dataset. Building upon UltraChat, we fine-tune a LLaMA model to create a powerful conversational model, UltraLLaMA. Our evaluations indicate that UltraLLaMA consistently outperforms other open-source models, including Vicuna, the previously recognized state-of-the-art open-source model. The dataset and the model will be publicly released\url{https://github.com/thunlp/UltraChat}.

We introduce AnyTool, a large language model agent designed to revolutionize the utilization of a vast array of tools in addressing user queries. We utilize over 16,000 APIs from Rapid API, operating under the assumption that a subset of these APIs could potentially resolve the queries. AnyTool primarily incorporates three elements: an API retriever with a hierarchical structure, a solver aimed at resolving user queries using a selected set of API candidates, and a self-reflection mechanism, which re-activates AnyTool if the initial solution proves impracticable. AnyTool is powered by the function calling feature of GPT-4, eliminating the need for training external modules. We also revisit the evaluation protocol introduced by previous works and identify a limitation in this protocol that leads to an artificially high pass rate. By revising the evaluation protocol to better reflect practical application scenarios, we introduce an additional benchmark, termed AnyToolBench. Experiments across various datasets demonstrate the superiority of our AnyTool over strong baselines such as ToolLLM and a GPT-4 variant tailored for tool utilization. For instance, AnyTool outperforms ToolLLM by +35.4% in terms of average pass rate on ToolBench. Code will be available at https://github.com/dyabel/AnyTool.

Programming with Generative AI (GenAI) models is a type of Neurosymbolic programming and has seen tremendous adoption across many domains. However, leveraging GenAI models in code today can be complex, counter-intuitive and often require specialized frameworks, leading to increased complexity. This is because it is currently unclear as to the right abstractions through which we should marry GenAI models with the nature of traditional programming code constructs. In this paper, we introduce a set of novel abstractions to help bridge the gap between Neuro- and symbolic programming. We introduce Meaning, a new specialized type that represents the underlying semantic value of traditional types (e.g., string). We make the case that GenAI models, LLMs in particular, should be reasoned as a meaning-type wrapped code construct at the language level. We formulate the problem of translation between meaning and traditional types and propose Automatic Meaning-Type Transformation (A-MTT), a runtime feature that abstracts this translation away from the developers by automatically converting between M eaning and types at the interface of LLM invocation. Leveraging this new set of code constructs and OTT, we demonstrate example implementation of neurosymbolic programs that seamlessly utilizes LLMs to solve problems in place of potentially complex traditional programming logic.

We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the learned algorithm into Python code. We test MIPS on a benchmark of 62 algorithmic tasks that can be learned by an RNN and find it highly complementary to GPT-4: MIPS solves 32 of them, including 13 that are not solved by GPT-4 (which also solves 30). MIPS uses an integer autoencoder to convert the RNN into a finite state machine, then applies Boolean or integer symbolic regression to capture the learned algorithm. As opposed to large language models, this program synthesis technique makes no use of (and is therefore not limited by) human training data such as algorithms and code from GitHub. We discuss opportunities and challenges for scaling up this approach to make machine-learned models more interpretable and trustworthy.

Prior work has shown that finetuning large language models (LLMs) using machine-generated instruction-following data enables such models to achieve remarkable zero-shot capabilities on new tasks, and no human-written instructions are needed. In this paper, we present the first attempt to use GPT-4 to generate instruction-following data for LLM finetuning. Our early experiments on instruction-tuned LLaMA models show that the 52K English and Chinese instruction-following data generated by GPT-4 leads to superior zero-shot performance on new tasks to the instruction-following data generated by previous state-of-the-art models. We also collect feedback and comparison data from GPT-4 to enable a comprehensive evaluation and reward model training. We make our data generated using GPT-4 as well as our codebase publicly available.

Generative AI and large language models hold great promise in enhancing computing education by powering next-generation educational technologies for introductory programming. Recent works have studied these models for different scenarios relevant to programming education; however, these works are limited for several reasons, as they typically consider already outdated models or only specific scenario(s). Consequently, there is a lack of a systematic study that benchmarks state-of-the-art models for a comprehensive set of programming education scenarios. In our work, we systematically evaluate two models, ChatGPT (based on GPT-3.5) and GPT-4, and compare their performance with human tutors for a variety of scenarios. We evaluate using five introductory Python programming problems and real-world buggy programs from an online platform, and assess performance using expert-based annotations. Our results show that GPT-4 drastically outperforms ChatGPT (based on GPT-3.5) and comes close to human tutors' performance for several scenarios. These results also highlight settings where GPT-4 still struggles, providing exciting future directions on developing techniques to improve the performance of these models.

Instruction tuning has emerged as a promising approach to enhancing large language models in following human instructions. It is shown that increasing the diversity and number of instructions in the training data can consistently enhance generalization performance, which facilitates a recent endeavor to collect various instructions and integrate existing instruction tuning datasets into larger collections. However, different users have their unique ways of expressing instructions, and there often exist variations across different datasets in the instruction styles and formats, i.e., format inconsistency. In this work, we study how format inconsistency may impact the performance of instruction tuning. We propose a framework called "Unified Instruction Tuning" (UIT), which calls OpenAI APIs for automatic format transfer among different instruction tuning datasets. We show that UIT successfully improves the generalization performance on unseen instructions, which highlights the importance of format consistency for instruction tuning. To make the UIT framework more practical, we further propose a novel perplexity-based denoising method to reduce the noise of automatic format transfer. We also train a smaller offline model that achieves comparable format transfer capability than OpenAI APIs to reduce costs in practice.

Large language models (LLMs) for code have become indispensable in various domains, including code generation, reasoning tasks and agent systems.While open-access code LLMs are increasingly approaching the performance levels of proprietary models, high-quality code LLMs suitable for rigorous scientific investigation, particularly those with reproducible data processing pipelines and transparent training protocols, remain limited. The scarcity is due to various challenges, including resource constraints, ethical considerations, and the competitive advantages of keeping models advanced. To address the gap, we introduce OpenCoder, a top-tier code LLM that not only achieves performance comparable to leading models but also serves as an ``open cookbook'' for the research community. Unlike most prior efforts, we release not only model weights and inference code, but also the reproducible training data, complete data processing pipeline, rigorous experimental ablation results, and detailed training protocols for open scientific research. Through this comprehensive release, we identify the key ingredients for building a top-tier code LLM: (1) code optimized heuristic rules for data cleaning and methods for data deduplication, (2) recall of text corpus related to code and (3) high-quality synthetic data in both annealing and supervised fine-tuning stages. By offering this level of openness, we aim to broaden access to all aspects of a top-tier code LLM, with OpenCoder serving as both a powerful model and an open foundation to accelerate research, and enable reproducible advancements in code AI.

Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring challenging applied mathematics problems that require analytical approximation techniques. These problems demand a combination of mathematical reasoning, computational tools, and subjective judgment, making them difficult for LLMs. Our framework auto-generates a large number of problems with solutions validated against numerical ground truths. We evaluate both open- and closed-source LLMs on HARDMath-mini, a sub-sampled test set of 366 problems, as well as on 40 word problems formulated in applied science contexts. Even leading closed-source models like GPT-4 achieve only 43.8% overall accuracy with few-shot Chain-of-Thought prompting, and all models demonstrate significantly lower performance compared to results on existing mathematics benchmark datasets. We additionally conduct a detailed error analysis to gain insights into the failure cases of LLMs. These results demonstrate limitations of current LLM performance on advanced graduate-level applied math problems and underscore the importance of datasets like HARDMath to advance mathematical abilities of LLMs.

Artificial intelligence (AI) methods have become critical in scientific applications to help accelerate scientific discovery. Large language models (LLMs) are being considered as a promising approach to address some of the challenging problems because of their superior generalization capabilities across domains. The effectiveness of the models and the accuracy of the applications is contingent upon their efficient execution on the underlying hardware infrastructure. Specialized AI accelerator hardware systems have recently become available for accelerating AI applications. However, the comparative performance of these AI accelerators on large language models has not been previously studied. In this paper, we systematically study LLMs on multiple AI accelerators and GPUs and evaluate their performance characteristics for these models. We evaluate these systems with (i) a micro-benchmark using a core transformer block, (ii) a GPT- 2 model, and (iii) an LLM-driven science use case, GenSLM. We present our findings and analyses of the models' performance to better understand the intrinsic capabilities of AI accelerators. Furthermore, our analysis takes into account key factors such as sequence lengths, scaling behavior, sparsity, and sensitivity to gradient accumulation steps.

This paper introduces Adaptive Computation Time (ACT), an algorithm that allows recurrent neural networks to learn how many computational steps to take between receiving an input and emitting an output. ACT requires minimal changes to the network architecture, is deterministic and differentiable, and does not add any noise to the parameter gradients. Experimental results are provided for four synthetic problems: determining the parity of binary vectors, applying binary logic operations, adding integers, and sorting real numbers. Overall, performance is dramatically improved by the use of ACT, which successfully adapts the number of computational steps to the requirements of the problem. We also present character-level language modelling results on the Hutter prize Wikipedia dataset. In this case ACT does not yield large gains in performance; however it does provide intriguing insight into the structure of the data, with more computation allocated to harder-to-predict transitions, such as spaces between words and ends of sentences. This suggests that ACT or other adaptive computation methods could provide a generic method for inferring segment boundaries in sequence data.

Code synthesis, which requires a deep understanding of complex natural language problem descriptions, generation of code instructions for complex algorithms and data structures, and the successful execution of comprehensive unit tests, presents a significant challenge. While large language models (LLMs) demonstrate impressive proficiency in natural language processing, their performance in code generation tasks remains limited. In this paper, we introduce a new approach to code generation tasks leveraging multi-agent prompting that uniquely replicates the full cycle of program synthesis as observed in human developers. Our framework, MapCoder, consists of four LLM agents specifically designed to emulate the stages of this cycle: recalling relevant examples, planning, code generation, and debugging. After conducting thorough experiments, with multiple LLM ablations and analyses across eight challenging competitive problem-solving and program synthesis benchmarks, MapCoder showcases remarkable code generation capabilities, achieving new state-of-the-art results (pass@1) on HumanEval (93.9%), MBPP (83.1%), APPS (22.0%), CodeContests (28.5%), and xCodeEval (45.3%). Moreover, our method consistently delivers superior performance across various programming languages and varying problem difficulties. We open-source our framework at https://github.com/Md-Ashraful-Pramanik/MapCoder.

We study the classic Text-to-Pattern Hamming Distances problem: given a pattern P of length m and a text T of length n, both over a polynomial-size alphabet, compute the Hamming distance between P and T[i, ., . , i+m-1] for every shift i, under the standard Word-RAM model with Theta(log n)-bit words. - We provide an O(nm) time Las Vegas randomized algorithm for this problem, beating the decades-old O(n m log m) running time [Abrahamson, SICOMP 1987]. We also obtain a deterministic algorithm, with a slightly higher O(nm(log mloglog m)^{1/4}) running time. Our randomized algorithm extends to the k-bounded setting, with running time Obig(n+nk{m}big), removing all the extra logarithmic factors from earlier algorithms [Gawrychowski and Uzna\'{n}ski, ICALP 2018; Chan, Golan, Kociumaka, Kopelowitz and Porat, STOC 2020]. - For the (1+epsilon)-approximate version of Text-to-Pattern Hamming Distances, we give an O(epsilon^{-0.93}n) time Monte Carlo randomized algorithm, beating the previous O(epsilon^{-1}n) running time [Kopelowitz and Porat, FOCS 2015; Kopelowitz and Porat, SOSA 2018]. Our approximation algorithm exploits a connection with 3SUM, and uses a combination of Fredman's trick, equality matrix product, and random sampling; in particular, we obtain new results on approximate counting versions of 3SUM and Exact Triangle, which may be of independent interest. Our exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion; in particular, we obtain a faster algorithm for computing the sumset of two integer sets, in the regime when the universe size is close to quadratic in the number of elements. We also prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3SUM.

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PLANSEARCH, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PLANSEARCH generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PLANSEARCH explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PLANSEARCH on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas.

Large Language Models (LLMs) have demonstrated remarkable success in various natural language processing and software engineering tasks, such as code generation. The LLMs are mainly utilized in the prompt-based zero/few-shot paradigm to guide the model in accomplishing the task. GPT-based models are one of the popular ones studied for tasks such as code comment generation or test generation. These tasks are `generative' tasks. However, there is limited research on the usage of LLMs for `non-generative' tasks such as classification using the prompt-based paradigm. In this preliminary exploratory study, we investigated the applicability of LLMs for Code Clone Detection (CCD), a non-generative task. By building a mono-lingual and cross-lingual CCD dataset derived from CodeNet, we first investigated two different prompts using ChatGPT to detect Type-4 code clones in Java-Java and Java-Ruby pairs in a zero-shot setting. We then conducted an analysis to understand the strengths and weaknesses of ChatGPT in CCD. ChatGPT surpasses the baselines in cross-language CCD attaining an F1-score of 0.877 and achieves comparable performance to fully fine-tuned models for mono-lingual CCD, with an F1-score of 0.878. Also, the prompt and the difficulty level of the problems has an impact on the performance of ChatGPT. Finally we provide insights and future directions based on our initial analysis

Language models are not accurate in numerical problems. Their architecture does not allow for anything less than a probabilistic next word. This paper introduces ComputeGPT: an approach of creating a chat model able to answer computational problems through running on-demand code. ComputeGPT converts each question to relevant code, runs the code, and returns the computed answer as part of the chat. We combine this approach with a local browser-based Python interpretation and fine-tuned prompts in order to achieve state-of-the-art efficiency on numerical problems and provide a suitable front-end and safe environment for the code to be executed in.

The burgeoning field of Large Language Models (LLMs), exemplified by sophisticated models like OpenAI's ChatGPT, represents a significant advancement in artificial intelligence. These models, however, bring forth substantial challenges in the high consumption of computational, memory, energy, and financial resources, especially in environments with limited resource capabilities. This survey aims to systematically address these challenges by reviewing a broad spectrum of techniques designed to enhance the resource efficiency of LLMs. We categorize methods based on their optimization focus: computational, memory, energy, financial, and network resources and their applicability across various stages of an LLM's lifecycle, including architecture design, pretraining, finetuning, and system design. Additionally, the survey introduces a nuanced categorization of resource efficiency techniques by their specific resource types, which uncovers the intricate relationships and mappings between various resources and corresponding optimization techniques. A standardized set of evaluation metrics and datasets is also presented to facilitate consistent and fair comparisons across different models and techniques. By offering a comprehensive overview of the current sota and identifying open research avenues, this survey serves as a foundational reference for researchers and practitioners, aiding them in developing more sustainable and efficient LLMs in a rapidly evolving landscape.

The class of tree-adjoining languages can be characterized by various two-level formalisms, consisting of a context-free grammar (CFG) or pushdown automaton (PDA) controlling another CFG or PDA. These four formalisms are equivalent to tree-adjoining grammars (TAG), linear indexed grammars (LIG), pushdown-adjoining automata (PAA), and embedded pushdown automata (EPDA). We define semiring-weighted versions of the above two-level formalisms, and we design new algorithms for computing their stringsums (the weight of all derivations of a string) and allsums (the weight of all derivations). From these, we also immediately obtain stringsum and allsum algorithms for TAG, LIG, PAA, and EPDA. For LIG, our algorithm is more time-efficient by a factor of O(n|N|) (where n is the string length and |N| is the size of the nonterminal set) and more space-efficient by a factor of O(|Gamma|) (where |Gamma| is the size of the stack alphabet) than the algorithm of Vijay-Shanker and Weir (1989). For EPDA, our algorithm is both more space-efficient and time-efficient than the algorithm of Alonso et al. (2001) by factors of O(|Gamma|^2) and O(|Gamma|^3), respectively. Finally, we give the first PAA stringsum and allsum algorithms.

Human intelligence emerged through the process of natural selection and evolution on Earth. We investigate what it would take to re-create this process in silico. While past work has often focused on low-level processes (such as simulating physics or chemistry), we instead take a more targeted approach, aiming to evolve agents that can accumulate open-ended culture and technologies across generations. Towards this, we present JaxLife: an artificial life simulator in which embodied agents, parameterized by deep neural networks, must learn to survive in an expressive world containing programmable systems. First, we describe the environment and show that it can facilitate meaningful Turing-complete computation. We then analyze the evolved emergent agents' behavior, such as rudimentary communication protocols, agriculture, and tool use. Finally, we investigate how complexity scales with the amount of compute used. We believe JaxLife takes a step towards studying evolved behavior in more open-ended simulations. Our code is available at https://github.com/luchris429/JaxLife

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general syntax of structural recursion, coupled with two different frameworks for understanding their semantics -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

Language models typically need to be trained or finetuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this work, we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate kNN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. On benchmarks including code and mathematics, we find that the model is capable of making use of newly defined functions and theorems during test time.

Large language models (LLMs) have demonstrated significant universal capabilities as few/zero-shot learners in various tasks due to their pre-training on vast amounts of text data, as exemplified by GPT-3, which boosted to InstrctGPT and ChatGPT, effectively following natural language instructions to accomplish real-world tasks. In this paper, we propose to introduce instruction tuning into multi-modal models, motivated by the Flamingo model's upstream interleaved format pretraining dataset. We adopt a similar approach to construct our MultI-Modal In-Context Instruction Tuning (MIMIC-IT) dataset. We then introduce Otter, a multi-modal model based on OpenFlamingo (open-sourced version of DeepMind's Flamingo), trained on MIMIC-IT and showcasing improved instruction-following ability and in-context learning. We also optimize OpenFlamingo's implementation for researchers, democratizing the required training resources from 1times A100 GPU to 4times RTX-3090 GPUs, and integrate both OpenFlamingo and Otter into Huggingface Transformers for more researchers to incorporate the models into their customized training and inference pipelines.

In the large language model (LLM) revolution, embedding is a key component of various systems. For example, it is used to retrieve knowledge or memories for LLMs, to build content moderation filters, etc. As such cases span from English to other natural or programming languages, from retrieval to classification and beyond, it is desirable to build a unified embedding model rather than dedicated ones for each scenario. In this work, we make an initial step towards this goal, demonstrating that multiple languages (both natural and programming) pre-trained transformer decoders can embed universally when finetuned on limited English data. We provide a comprehensive practice with thorough evaluations. On English MTEB, our models achieve competitive performance on different embedding tasks by minimal training data. On other benchmarks, such as multilingual classification and code search, our models (without any supervision) perform comparably to, or even surpass heavily supervised baselines and/or APIs. These results provide evidence of a promising path towards building powerful unified embedders that can be applied across tasks and languages.

The recent progress of AI can be largely attributed to large language models (LLMs). However, their escalating memory requirements introduce challenges for machine learning (ML) researchers and engineers. Addressing this requires developers to partition a large model to distribute it across multiple GPUs or TPUs. This necessitates considerable coding and intricate configuration efforts with existing model parallel tools, such as Megatron-LM, DeepSpeed, and Alpa. These tools require users' expertise in machine learning systems (MLSys), creating a bottleneck in LLM development, particularly for developers without MLSys background. In this work, we present Redco, a lightweight and user-friendly tool crafted to automate distributed training and inference for LLMs, as well as to simplify ML pipeline development. The design of Redco emphasizes two key aspects. Firstly, to automate model parallism, our study identifies two straightforward rules to generate tensor parallel strategies for any given LLM. Integrating these rules into Redco facilitates effortless distributed LLM training and inference, eliminating the need of additional coding or complex configurations. We demonstrate the effectiveness by applying Redco on a set of LLM architectures, such as GPT-J, LLaMA, T5, and OPT, up to the size of 66B. Secondly, we propose a mechanism that allows for the customization of diverse ML pipelines through the definition of merely three functions, eliminating redundant and formulaic code like multi-host related processing. This mechanism proves adaptable across a spectrum of ML algorithms, from foundational language modeling to complex algorithms like meta-learning and reinforcement learning. Consequently, Redco implementations exhibit much fewer code lines compared to their official counterparts.

Pre-training Large Language Models (LLMs) on high-quality, meticulously curated datasets is widely recognized as critical for enhancing their performance and generalization capabilities. This study explores the untapped potential of Common Crawl as a comprehensive and flexible resource for pre-training LLMs, addressing both general-purpose language understanding and specialized domain knowledge. We introduce RedStone, an innovative and scalable pipeline engineered to extract and process data from Common Crawl, facilitating the creation of extensive and varied pre-training datasets. Unlike traditional datasets, which often require expensive curation and domain-specific expertise, RedStone leverages the breadth of Common Crawl to deliver datasets tailored to a wide array of domains. In this work, we exemplify its capability by constructing pre-training datasets across multiple fields, including general language understanding, code, mathematics, and question-answering tasks. The flexibility of RedStone allows for easy adaptation to other specialized domains, significantly lowering the barrier to creating valuable domain-specific datasets. Our findings demonstrate that Common Crawl, when harnessed through effective pipelines like RedStone, can serve as a rich, renewable source of pre-training data, unlocking new avenues for domain adaptation and knowledge discovery in LLMs. This work also underscores the importance of innovative data acquisition strategies and highlights the role of web-scale data as a powerful resource in the continued evolution of LLMs. RedStone code and data samples will be publicly available at https://aka.ms/redstone.

Despite the tremendous success, existing machine learning models still fall short of human-like systematic generalization -- learning compositional rules from limited data and applying them to unseen combinations in various domains. We propose Neural-Symbolic Recursive Machine (NSR) to tackle this deficiency. The core representation of NSR is a Grounded Symbol System (GSS) with combinatorial syntax and semantics, which entirely emerges from training data. Akin to the neuroscience studies suggesting separate brain systems for perceptual, syntactic, and semantic processing, NSR implements analogous separate modules of neural perception, syntactic parsing, and semantic reasoning, which are jointly learned by a deduction-abduction algorithm. We prove that NSR is expressive enough to model various sequence-to-sequence tasks. Superior systematic generalization is achieved via the inductive biases of equivariance and recursiveness embedded in NSR. In experiments, NSR achieves state-of-the-art performance in three benchmarks from different domains: SCAN for semantic parsing, PCFG for string manipulation, and HINT for arithmetic reasoning. Specifically, NSR achieves 100% generalization accuracy on SCAN and PCFG and outperforms state-of-the-art models on HINT by about 23%. Our NSR demonstrates stronger generalization than pure neural networks due to its symbolic representation and inductive biases. NSR also demonstrates better transferability than existing neural-symbolic approaches due to less domain-specific knowledge required.

Communicating state machines provide a formal foundation for distributed computation. Unfortunately, they are Turing-complete and, thus, challenging to analyse. In this paper, we classify restrictions on channels which have been proposed to work around the undecidability of verification questions. We compare half-duplex communication, existential B-boundedness, and k-synchronisability. These restrictions do not prevent the communication channels from growing arbitrarily large but still restrict the power of the model. Each restriction gives rise to a set of languages so, for every pair of restrictions, we check whether one subsumes the other or if they are incomparable. We investigate their relationship in two different contexts: first, the one of communicating state machines, and, second, the one of communication protocol specifications using high-level message sequence charts. Surprisingly, these two contexts yield different conclusions. In addition, we integrate multiparty session types, another approach to specify communication protocols, into our classification. We show that multiparty session type languages are half-duplex, existentially 1-bounded, and 1-synchronisable. To~show this result, we provide the first formal embedding of multiparty session types into high-level message sequence charts.

We introduce RecurrentGemma, an open language model which uses Google's novel Griffin architecture. Griffin combines linear recurrences with local attention to achieve excellent performance on language. It has a fixed-sized state, which reduces memory use and enables efficient inference on long sequences. We provide a pre-trained model with 2B non-embedding parameters, and an instruction tuned variant. Both models achieve comparable performance to Gemma-2B despite being trained on fewer tokens.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

Large language models (LLMs) have recently demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed to prompting methods such as "chain-of-thought'', which employ LLMs for both understanding the problem description by decomposing it into steps, as well as solving each step of the problem. While LLMs seem to be adept at this sort of step-by-step decomposition, LLMs often make logical and arithmetic mistakes in the solution part, even when the problem is decomposed correctly. In this paper, we present Program-Aided Language models (PAL): a novel approach that uses the LLM to read natural language problems and generate programs as the intermediate reasoning steps, but offloads the solution step to a runtime such as a Python interpreter. With PAL, decomposing the natural language problem into runnable steps remains the only learning task for the LLM, while solving is delegated to the interpreter. We demonstrate this synergy between a neural LLM and a symbolic interpreter across 13 mathematical, symbolic, and algorithmic reasoning tasks from BIG-Bench Hard and other benchmarks. In all these natural language reasoning tasks, generating code using an LLM and reasoning using a Python interpreter leads to more accurate results than much larger models. For example, PAL using Codex achieves state-of-the-art few-shot accuracy on the GSM8K benchmark of math word problems, surpassing PaLM-540B which uses chain-of-thought by absolute 15% top-1. Our code and data are publicly available at http://reasonwithpal.com/ .

In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide array of text-centric tasks. However, their `large' scale introduces significant computational and storage challenges, particularly in managing the key-value states of the transformer, which limits their wider applicability. Therefore, we propose to adaptively release resources from caches and rebuild the necessary key-value states. Particularly, we accomplish this by a lightweight controller module to approximate an ideal top-K sparse attention. This module retains the tokens with the highest top-K attention weights and simultaneously rebuilds the discarded but necessary tokens, which may become essential for future decoding. Comprehensive experiments in natural language generation and modeling reveal that our method is not only competitive with full attention in terms of performance but also achieves a significant throughput improvement of up to 221.8%. The code for replication is available on the https://github.com/WHUIR/ADORE.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including embedding edit operations, non-linear functions, function calls, program counters, and conditional branches. Using these building blocks, we emulate a small instruction-set computer. This allows us to map iterative algorithms to programs that can be executed by a looped, 13-layer transformer. We show how this transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and in-context learning algorithms that employ backpropagation. Our work highlights the versatility of the attention mechanism, and demonstrates that even shallow transformers can execute full-fledged, general-purpose programs.

In this paper we look at the ability of recent large language models (LLMs) at solving mathematical problems in combinatorics. We compare models LLaMA-2, LLaMA-3.1, GPT-4, and Mixtral against each other and against human pupils and undergraduates with prior experience in mathematical olympiads. To facilitate these comparisons we introduce the Combi-Puzzles dataset, which contains 125 problem variants based on 25 combinatorial reasoning problems. Each problem is presented in one of five distinct forms, created by systematically manipulating the problem statements through adversarial additions, numeric parameter changes, and linguistic obfuscation. Our variations preserve the mathematical core and are designed to measure the generalisability of LLM problem-solving abilities, while also increasing confidence that problems are submitted to LLMs in forms that have not been seen as training instances. We found that a model based on GPT-4 outperformed all other models in producing correct responses, and performed significantly better in the mathematical variation of the problems than humans. We also found that modifications to problem statements significantly impact the LLM's performance, while human performance remains unaffected.

We introduce meta-prompting, an effective scaffolding technique designed to enhance the functionality of language models (LMs). This approach transforms a single LM into a multi-faceted conductor, adept at managing and integrating multiple independent LM queries. By employing high-level instructions, meta-prompting guides the LM to break down complex tasks into smaller, more manageable subtasks. These subtasks are then handled by distinct "expert" instances of the same LM, each operating under specific, tailored instructions. Central to this process is the LM itself, in its role as the conductor, which ensures seamless communication and effective integration of the outputs from these expert models. It additionally employs its inherent critical thinking and robust verification processes to refine and authenticate the end result. This collaborative prompting approach empowers a single LM to simultaneously act as a comprehensive orchestrator and a panel of diverse experts, significantly enhancing its performance across a wide array of tasks. The zero-shot, task-agnostic nature of meta-prompting greatly simplifies user interaction by obviating the need for detailed, task-specific instructions. Furthermore, our research demonstrates the seamless integration of external tools, such as a Python interpreter, into the meta-prompting framework, thereby broadening its applicability and utility. Through rigorous experimentation with GPT-4, we establish the superiority of meta-prompting over conventional scaffolding methods: When averaged across all tasks, including the Game of 24, Checkmate-in-One, and Python Programming Puzzles, meta-prompting, augmented with a Python interpreter functionality, surpasses standard prompting by 17.1%, expert (dynamic) prompting by 17.3%, and multipersona prompting by 15.2%.

We find that, simply via a sampling-and-voting method, the performance of large language models (LLMs) scales with the number of agents instantiated. Also, this method is orthogonal to existing complicated methods to further enhance LLMs, while the degree of enhancement is correlated to the task difficulty. We conduct comprehensive experiments on a wide range of LLM benchmarks to verify the presence of our finding, and to study the properties that can facilitate its occurrence. Our code is publicly available at: https://anonymous.4open.science/r/more_agent_is_all_you_need.

Programming is a powerful and ubiquitous problem-solving tool. Developing systems that can assist programmers or even generate programs independently could make programming more productive and accessible, yet so far incorporating innovations in AI has proven challenging. Recent large-scale language models have demonstrated an impressive ability to generate code, and are now able to complete simple programming tasks. However, these models still perform poorly when evaluated on more complex, unseen problems that require problem-solving skills beyond simply translating instructions into code. For example, competitive programming problems which require an understanding of algorithms and complex natural language remain extremely challenging. To address this gap, we introduce AlphaCode, a system for code generation that can create novel solutions to these problems that require deeper reasoning. In simulated evaluations on recent programming competitions on the Codeforces platform, AlphaCode achieved on average a ranking of top 54.3% in competitions with more than 5,000 participants. We found that three key components were critical to achieve good and reliable performance: (1) an extensive and clean competitive programming dataset for training and evaluation, (2) large and efficient-to-sample transformer-based architectures, and (3) large-scale model sampling to explore the search space, followed by filtering based on program behavior to a small set of submissions.

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with relational data. In this work, we study the ability of transformer networks to simulate algorithms on graphs from a theoretical perspective. The architecture that we utilize is a looped transformer with extra attention heads that interact with the graph. We prove by construction that this architecture can simulate algorithms such as Dijkstra's shortest path algorithm, Breadth- and Depth-First Search, and Kosaraju's strongly connected components algorithm. The width of the network does not increase with the size of the input graph, which implies that the network can simulate the above algorithms for any graph. Despite this property, we show that there is a limit to simulation in our solution due to finite precision. Finally, we show a Turing Completeness result with constant width when the extra attention heads are utilized.

We present the Chinese Elementary School Math Word Problems (CMATH) dataset, comprising 1.7k elementary school-level math word problems with detailed annotations, source from actual Chinese workbooks and exams. This dataset aims to provide a benchmark tool for assessing the following question: to what grade level of elementary school math do the abilities of popular large language models (LLMs) correspond? We evaluate a variety of popular LLMs, including both commercial and open-source options, and discover that only GPT-4 achieves success (accuracy geq 60\%) across all six elementary school grades, while other models falter at different grade levels. Furthermore, we assess the robustness of several top-performing LLMs by augmenting the original problems in the CMATH dataset with distracting information. Our findings reveal that GPT-4 is able to maintains robustness, while other model fail. We anticipate that our study will expose limitations in LLMs' arithmetic and reasoning capabilities, and promote their ongoing development and advancement.

Code is increasingly becoming a core data modality of modern machine learning research impacting not only the way we write code with conversational agents like OpenAI's ChatGPT, Google's Bard, or Anthropic's Claude, the way we translate code from one language into another, but also the compiler infrastructure underlying the language. While modeling approaches may vary and representations differ, the targeted tasks often remain the same within the individual classes of models. Relying solely on the ability of modern models to extract information from unstructured code does not take advantage of 70 years of programming language and compiler development by not utilizing the structure inherent to programs in the data collection. This detracts from the performance of models working over a tokenized representation of input code and precludes the use of these models in the compiler itself. To work towards the first intermediate representation (IR) based models, we fully utilize the LLVM compiler infrastructure, shared by a number of languages, to generate a 182B token dataset of LLVM IR. We generated this dataset from programming languages built on the shared LLVM infrastructure, including Rust, Swift, Julia, and C/C++, by hooking into LLVM code generation either through the language's package manager or the compiler directly to extract the dataset of intermediate representations from production grade programs. Statistical analysis proves the utility of our dataset not only for large language model training, but also for the introspection into the code generation process itself with the dataset showing great promise for machine-learned compiler components.

Language models (LMs) built upon deep neural networks (DNNs) have recently demonstrated breakthrough effectiveness in software engineering tasks such as code generation, completion, and repair. This has paved the way for the emergence of LM-based code optimization techniques, which are crucial for enhancing the performance of existing programs, such as accelerating program execution time. However, a comprehensive survey dedicated to this specific application has been lacking. To fill this gap, we present a systematic literature review of over 50 primary studies, identifying emerging trends and addressing 11 specialized questions. Our findings reveal five critical open challenges, such as balancing model complexity with practical usability, cross-language/performance generalizability, and building trust in AI-driven solutions. Furthermore, we provide eight future research directions to facilitate more efficient, robust, and reliable LM-based code optimization. Thereby, this study aims to provide actionable insights and foundational references for both researchers and practitioners in this rapidly evolving field.

The impressive capabilities of Large Language Models (LLMs) across diverse tasks are now well-established, yet their effective deployment necessitates careful hyperparameter optimization. Through extensive empirical studies involving grid searches across diverse configurations, we discover universal scaling laws governing these hyperparameters: optimal learning rate follows a power-law relationship with both model parameters and data sizes, while optimal batch size scales primarily with data sizes. Our analysis reveals a convex optimization landscape for hyperparameters under fixed models and data size conditions. This convexity implies an optimal hyperparameter plateau. We contribute a universal, plug-and-play optimal hyperparameter tool for the community. Its estimated values on the test set are merely 0.07\% away from the globally optimal LLM performance found via an exhaustive search. These laws demonstrate remarkable robustness across variations in model sparsity, training data distribution, and model shape. To our best known, this is the first work that unifies different model shapes and structures, such as Mixture-of-Experts models and dense transformers, as well as establishes optimal hyperparameter scaling laws across diverse data distributions. This exhaustive optimization process demands substantial computational resources, utilizing nearly one million NVIDIA H800 GPU hours to train 3,700 LLMs of varying sizes and hyperparameters from scratch and consuming approximately 100 trillion tokens in total. To facilitate reproducibility and further research, we will progressively release all loss measurements and model checkpoints through our designated repository https://step-law.github.io/

The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (ibm\_fez) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of approx0.37% and approx0.31%, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states |H_Lrangle and |T_Lrangle achieve fidelities of 0.8806pm0.0002 and 0.8665pm0.0003, respectively, which are both above the magic state distillation threshold. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as 0.8356pm0.0003. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.

By conditioning on natural language instructions, large language models (LLMs) have displayed impressive capabilities as general-purpose computers. However, task performance depends significantly on the quality of the prompt used to steer the model, and most effective prompts have been handcrafted by humans. Inspired by classical program synthesis and the human approach to prompt engineering, we propose Automatic Prompt Engineer (APE) for automatic instruction generation and selection. In our method, we treat the instruction as the "program," optimized by searching over a pool of instruction candidates proposed by an LLM in order to maximize a chosen score function. To evaluate the quality of the selected instruction, we evaluate the zero-shot performance of another LLM following the selected instruction. Experiments on 24 NLP tasks show that our automatically generated instructions outperform the prior LLM baseline by a large margin and achieve better or comparable performance to the instructions generated by human annotators on 19/24 tasks. We conduct extensive qualitative and quantitative analyses to explore the performance of APE. We show that APE-engineered prompts can be applied to steer models toward truthfulness and/or informativeness, as well as to improve few-shot learning performance by simply prepending them to standard in-context learning prompts. Please check out our webpage at https://sites.google.com/view/automatic-prompt-engineer.

The increasing adoption and commercialization of generalized Large Language Models (LLMs) have profoundly impacted various aspects of our daily lives. Initially embraced by the computer science community, the versatility of LLMs has found its way into diverse domains. In particular, the software engineering realm has witnessed the most transformative changes. With LLMs increasingly serving as AI Pair Programming Assistants spurred the development of specialized models aimed at aiding software engineers. Although this new paradigm offers numerous advantages, it also presents critical challenges and open problems. To identify the potential and prevailing obstacles, we systematically reviewed contemporary scholarly publications, emphasizing the perspectives of software developers and usability concerns. Preliminary findings underscore pressing concerns about data privacy, bias, and misinformation. Additionally, we identified several usability challenges, including prompt engineering, increased cognitive demands, and mistrust. Finally, we introduce 12 open problems that we have identified through our survey, covering these various domains.

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 (ge 175B) to T5 variants (le 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We further give comprehensive discussions about important design choices for better generalization, including the tuning data format, the start model checkpoint, and a new model selection method. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs.

The objective of pre-trained language models is to learn contextual representations of textual data. Pre-trained language models have become mainstream in natural language processing and code modeling. Using probes, a technique to study the linguistic properties of hidden vector spaces, previous works have shown that these pre-trained language models encode simple linguistic properties in their hidden representations. However, none of the previous work assessed whether these models encode the whole grammatical structure of a programming language. In this paper, we prove the existence of a syntactic subspace, lying in the hidden representations of pre-trained language models, which contain the syntactic information of the programming language. We show that this subspace can be extracted from the models' representations and define a novel probing method, the AST-Probe, that enables recovering the whole abstract syntax tree (AST) of an input code snippet. In our experimentations, we show that this syntactic subspace exists in five state-of-the-art pre-trained language models. In addition, we highlight that the middle layers of the models are the ones that encode most of the AST information. Finally, we estimate the optimal size of this syntactic subspace and show that its dimension is substantially lower than those of the models' representation spaces. This suggests that pre-trained language models use a small part of their representation spaces to encode syntactic information of the programming languages.

Code generation by Llama 3.1 models, such as Meta's Llama 3.1 405B, represents a significant advancement in the field of artificial intelligence, particularly in natural language processing and programming automation. This paper explores the capabilities and applications of Llama-driven code generation, highlighting its ability to translate natural language prompts into executable code across multiple programming languages. Key features include contextual awareness, multi-language support, and enhanced debugging and optimization functionalities. By examining these aspects, we illustrate how Llama can serve as a versatile tool for developers of all skill levels, improving productivity and efficiency in software development. The potential implications for education, industry, and the future of coding practices are also discussed, underscoring the transformative impact of AI in programming. Experimentation shows that while Llama 3.1 405B performs well with simple algorithmic and data structure based problems, it still struggles with problems on Quantum Computing, Bioinformatics, and Artificial Intelligence.

The prominent large language models (LLMs) of today differ from past language models not only in size, but also in the fact that they are trained on a combination of natural language and formal language (code). As a medium between humans and computers, code translates high-level goals into executable steps, featuring standard syntax, logical consistency, abstraction, and modularity. In this survey, we present an overview of the various benefits of integrating code into LLMs' training data. Specifically, beyond enhancing LLMs in code generation, we observe that these unique properties of code help (i) unlock the reasoning ability of LLMs, enabling their applications to a range of more complex natural language tasks; (ii) steer LLMs to produce structured and precise intermediate steps, which can then be connected to external execution ends through function calls; and (iii) take advantage of code compilation and execution environment, which also provides diverse feedback for model improvement. In addition, we trace how these profound capabilities of LLMs, brought by code, have led to their emergence as intelligent agents (IAs) in situations where the ability to understand instructions, decompose goals, plan and execute actions, and refine from feedback are crucial to their success on downstream tasks. Finally, we present several key challenges and future directions of empowering LLMs with code.

In this work we explore recent advances in instruction-tuning language models on a range of open instruction-following datasets. Despite recent claims that open models can be on par with state-of-the-art proprietary models, these claims are often accompanied by limited evaluation, making it difficult to compare models across the board and determine the utility of various resources. We provide a large set of instruction-tuned models from 6.7B to 65B parameters in size, trained on 12 instruction datasets ranging from manually curated (e.g., OpenAssistant) to synthetic and distilled (e.g., Alpaca) and systematically evaluate them on their factual knowledge, reasoning, multilinguality, coding, and open-ended instruction following abilities through a collection of automatic, model-based, and human-based metrics. We further introduce T\"ulu, our best performing instruction-tuned model suite finetuned on a combination of high-quality open resources. Our experiments show that different instruction-tuning datasets can uncover or enhance specific skills, while no single dataset (or combination) provides the best performance across all evaluations. Interestingly, we find that model and human preference-based evaluations fail to reflect differences in model capabilities exposed by benchmark-based evaluations, suggesting the need for the type of systemic evaluation performed in this work. Our evaluations show that the best model in any given evaluation reaches on average 83% of ChatGPT performance, and 68% of GPT-4 performance, suggesting that further investment in building better base models and instruction-tuning data is required to close the gap. We release our instruction-tuned models, including a fully finetuned 65B T\"ulu, along with our code, data, and evaluation framework at https://github.com/allenai/open-instruct to facilitate future research.

We initiate a formal investigation into the design and analysis of LLM-based algorithms, i.e. algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of LLMs. While LLM-based algorithms, ranging from basic LLM calls with prompt engineering to complicated LLM-powered agent systems and compound AI systems, have achieved remarkable empirical success, the design and optimization of them have mostly relied on heuristics and trial-and-errors, which is largely due to a lack of formal and analytical study for these algorithms. To fill this gap, we start by identifying the computational-graph representation of LLM-based algorithms, the design principle of task decomposition, and some key abstractions, which then facilitate our formal analysis for the accuracy and efficiency of LLM-based algorithms, despite the black-box nature of LLMs. Through extensive analytical and empirical investigation in a series of case studies, we demonstrate that the proposed framework is broadly applicable to a wide range of scenarios and diverse patterns of LLM-based algorithms, such as parallel, hierarchical and recursive task decomposition. Our proposed framework holds promise for advancing LLM-based algorithms, by revealing the reasons behind curious empirical phenomena, guiding the choices of hyperparameters, predicting the empirical performance of algorithms, and inspiring new algorithm design. To promote further study of LLM-based algorithms, we release our source code at https://github.com/modelscope/agentscope/tree/main/examples/paper_llm_based_algorithm.

Large language models (LLMs) have shown remarkable improvements in reasoning and many existing benchmarks have been addressed by models such as o1 and o3 either fully or partially. However, a majority of these benchmarks emphasize deductive reasoning, including mathematical and coding tasks in which rules such as mathematical axioms or programming syntax are clearly defined, based on which LLMs can plan and apply these rules to arrive at a solution. In contrast, inductive reasoning, where one infers the underlying rules from observed data, remains less explored. Such inductive processes lie at the heart of scientific discovery, as they enable researchers to extract general principles from empirical observations. To assess whether LLMs possess this capacity, we introduce InductionBench, a new benchmark designed to evaluate the inductive reasoning ability of LLMs. Our experimental findings reveal that even the most advanced models available struggle to master the simplest complexity classes within the subregular hierarchy of functions, highlighting a notable deficiency in current LLMs' inductive reasoning capabilities. Coda and data are available https://github.com/Wenyueh/inductive_reasoning_benchmark.

Large language models (LLMs) have attracted considerable attention in various fields for their cost-effective solutions to diverse challenges, especially with advancements in instruction tuning and quantization. E-commerce, with its complex tasks and extensive product-user interactions, presents a promising application area for LLMs. However, the domain-specific concepts and knowledge inherent in e-commerce pose significant challenges for adapting general LLMs. To address this issue, we developed EC-Guide https://github.com/fzp0424/EC-Guide-KDDUP-2024, a comprehensive e-commerce guide for instruction tuning and quantization of LLMs. We also heuristically integrated Chain-of-Thought (CoT) during inference to enhance arithmetic performance. Our approach achieved the 2nd place in Track 2 and 5th place in Track 5 at the Amazon KDD Cup'24 https://www.aicrowd.com/challenges/amazon-kdd-cup-2024-multi-task-online-shopping-challenge-for-llms. Additionally, our solution is model-agnostic, enabling effective scalability across larger systems.

Recent advancements in large language models (LLMs) have led to significant breakthroughs in mathematical reasoning capabilities. However, existing benchmarks like GSM8K or MATH are now being solved with high accuracy (e.g., OpenAI o1 achieves 94.8% on MATH dataset), indicating their inadequacy for truly challenging these models. To bridge this gap, we propose a comprehensive and challenging benchmark specifically designed to assess LLMs' mathematical reasoning at the Olympiad level. Unlike existing Olympiad-related benchmarks, our dataset focuses exclusively on mathematics and comprises a vast collection of 4428 competition-level problems with rigorous human annotation. These problems are meticulously categorized into over 33 sub-domains and span more than 10 distinct difficulty levels, enabling a holistic assessment of model performance in Olympiad-mathematical reasoning. Furthermore, we conducted an in-depth analysis based on this benchmark. Our experimental results show that even the most advanced models, OpenAI o1-mini and OpenAI o1-preview, struggle with highly challenging Olympiad-level problems, with 60.54% and 52.55% accuracy, highlighting significant challenges in Olympiad-level mathematical reasoning.

Various jailbreak attacks have been proposed to red-team Large Language Models (LLMs) and revealed the vulnerable safeguards of LLMs. Besides, some methods are not limited to the textual modality and extend the jailbreak attack to Multimodal Large Language Models (MLLMs) by perturbing the visual input. However, the absence of a universal evaluation benchmark complicates the performance reproduction and fair comparison. Besides, there is a lack of comprehensive evaluation of closed-source state-of-the-art (SOTA) models, especially MLLMs, such as GPT-4V. To address these issues, this work first builds a comprehensive jailbreak evaluation dataset with 1445 harmful questions covering 11 different safety policies. Based on this dataset, extensive red-teaming experiments are conducted on 11 different LLMs and MLLMs, including both SOTA proprietary models and open-source models. We then conduct a deep analysis of the evaluated results and find that (1) GPT4 and GPT-4V demonstrate better robustness against jailbreak attacks compared to open-source LLMs and MLLMs. (2) Llama2 and Qwen-VL-Chat are more robust compared to other open-source models. (3) The transferability of visual jailbreak methods is relatively limited compared to textual jailbreak methods. The dataset and code can be found here https://anonymous.4open.science/r/red_teaming_gpt4-C1CE/README.md .

Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities, as evidenced by its impressive accuracy of 97.7% and 72.0% on the GSM8K and MATH benchmarks, respectively, when selecting the best response from 256 random generations. The primary issue with the current base model is the difficulty in consistently eliciting its inherent mathematical capabilities. Notably, the accuracy for the first answer drops to 49.5% and 7.9% on the GSM8K and MATH benchmarks, respectively. We find that simply scaling up the SFT data can significantly enhance the reliability of generating correct answers. However, the potential for extensive scaling is constrained by the scarcity of publicly available math questions. To overcome this limitation, we employ synthetic data, which proves to be nearly as effective as real data and shows no clear saturation when scaled up to approximately one million samples. This straightforward approach achieves an accuracy of 82.6% on GSM8K and 40.6% on MATH using LLaMA-2 7B models, surpassing previous models by 14.2% and 20.8%, respectively. We also provide insights into scaling behaviors across different reasoning complexities and error types.

Large language models have shown promising performance in code generation benchmarks. However, a considerable divide exists between these benchmark achievements and their practical applicability, primarily attributed to real-world programming's reliance on pre-existing libraries. Instead of evaluating LLMs to code from scratch, this work aims to propose a new evaluation setup where LLMs use open-source libraries to finish machine learning tasks. Therefore, we propose ML-Bench, an expansive benchmark developed to assess the effectiveness of LLMs in leveraging existing functions in open-source libraries. Consisting of 10044 samples spanning 130 tasks over 14 notable machine learning GitHub repositories. In this setting, given a specific machine learning task instruction and the accompanying README in a codebase, an LLM is tasked to generate code to accomplish the task. This necessitates the comprehension of long and language-code interleaved documents, as well as the understanding of complex cross-file code structures, introducing new challenges. Notably, while GPT-4 exhibits remarkable improvement over other LLMs, it manages to accomplish only 39.73\% of the tasks, leaving a huge space for improvement. We address these challenges by proposing ML-Agent, designed to effectively navigate the codebase, locate documentation, retrieve code, and generate executable code. Empirical results demonstrate that ML-Agent, built upon GPT-4, results in further improvements. Code, data, and models are available at https://ml-bench.github.io/.

We release and introduce the TigerBot family of large language models (LLMs), consisting of base and chat models, sized from 7, 13, 70 and 180 billion parameters. We develop our models embarking from Llama-2 and BLOOM, and push the boundary further in data, training algorithm, infrastructure, and application tools. Our models yield meaningful performance gain over SOTA open-source models, e.g., Llama-2, specifically 6\% gain in English and 20\% gain in Chinese. TigerBot model family also achieves leading performance in major academic and industrial benchmarks and leaderboards. We believe that TigerBot represents just a snapshot of lightning-fast progression in LLM open-source community. Therefore, we are thrilled to give back by publicly releasing our models and reporting our approach behind, with additional emphases on building SOTA LLMs in a democratized way and making LLMs of use in real-world applications.

Large Language Models (LLMs) have made significant progress in advancing artificial general intelligence (AGI), leading to the development of increasingly large models such as GPT-4 and LLaMA-405B. However, scaling up model sizes results in exponentially higher computational costs and energy consumption, making these models impractical for academic researchers and businesses with limited resources. At the same time, Small Models (SMs) are frequently used in practical settings, although their significance is currently underestimated. This raises important questions about the role of small models in the era of LLMs, a topic that has received limited attention in prior research. In this work, we systematically examine the relationship between LLMs and SMs from two key perspectives: Collaboration and Competition. We hope this survey provides valuable insights for practitioners, fostering a deeper understanding of the contribution of small models and promoting more efficient use of computational resources. The code is available at https://github.com/tigerchen52/role_of_small_models

Large Language Models (LLMs) have shown excellent performance in language understanding, text generation, code synthesis, and many other tasks, while they still struggle in complex multi-step reasoning problems, such as mathematical reasoning. In this paper, through a newly proposed arithmetical puzzle problem, we show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that not only the model can reach a zero-shot pass@1 at 0.44 on the in-domain dataset, it also demonstrates certain generalization capabilities on the out-of-domain datasets. Specifically, this paper has designed two out-of-domain datasets in the form of extending the numerical range and the composing components of the arithmetical puzzle problem separately. The fine-tuned models have shown encouraging performance on these two far more difficult tasks with the zero-shot pass@1 at 0.33 and 0.35, respectively.

Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success and become a milestone in the field of artificial intelligence (AI). Owing to sophisticated pre-training objectives and huge model parameters, large-scale PTMs can effectively capture knowledge from massive labeled and unlabeled data. By storing knowledge into huge parameters and fine-tuning on specific tasks, the rich knowledge implicitly encoded in huge parameters can benefit a variety of downstream tasks, which has been extensively demonstrated via experimental verification and empirical analysis. It is now the consensus of the AI community to adopt PTMs as backbone for downstream tasks rather than learning models from scratch. In this paper, we take a deep look into the history of pre-training, especially its special relation with transfer learning and self-supervised learning, to reveal the crucial position of PTMs in the AI development spectrum. Further, we comprehensively review the latest breakthroughs of PTMs. These breakthroughs are driven by the surge of computational power and the increasing availability of data, towards four important directions: designing effective architectures, utilizing rich contexts, improving computational efficiency, and conducting interpretation and theoretical analysis. Finally, we discuss a series of open problems and research directions of PTMs, and hope our view can inspire and advance the future study of PTMs.

"An idea is nothing more nor less than a new combination of old elements" (Young, J.W.). The widespread adoption of Large Language Models (LLMs) and publicly available ChatGPT have marked a significant turning point in the integration of Artificial Intelligence (AI) into people's everyday lives. This study explores the capability of LLMs in generating novel research ideas based on information from research papers. We conduct a thorough examination of 4 LLMs in five domains (e.g., Chemistry, Computer, Economics, Medical, and Physics). We found that the future research ideas generated by Claude-2 and GPT-4 are more aligned with the author's perspective than GPT-3.5 and Gemini. We also found that Claude-2 generates more diverse future research ideas than GPT-4, GPT-3.5, and Gemini 1.0. We further performed a human evaluation of the novelty, relevancy, and feasibility of the generated future research ideas. This investigation offers insights into the evolving role of LLMs in idea generation, highlighting both its capability and limitations. Our work contributes to the ongoing efforts in evaluating and utilizing language models for generating future research ideas. We make our datasets and codes publicly available.

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To automate problem formulation and solving, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of approach suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, the model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming, and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.

The recent trend of using Large Language Models (LLMs) as intelligent agents in real-world applications underscores the necessity for comprehensive evaluations of their capabilities, particularly in complex scenarios involving planning, creating, and using tools. However, existing benchmarks typically focus on simple synthesized queries that do not reflect real-world complexity, thereby offering limited perspectives in evaluating tool utilization. To address this issue, we present UltraTool, a novel benchmark designed to improve and evaluate LLMs' ability in tool utilization within real-world scenarios. UltraTool focuses on the entire process of using tools - from planning and creating to applying them in complex tasks. It emphasizes real-world complexities, demanding accurate, multi-step planning for effective problem-solving. A key feature of UltraTool is its independent evaluation of planning with natural language, which happens before tool usage and simplifies the task solving by mapping out the intermediate steps. Thus, unlike previous work, it eliminates the restriction of pre-defined toolset during planning. Through extensive experiments on various LLMs, we offer novel insights into the evaluation of capabilities of LLMs in tool utilization, thereby contributing a fresh perspective to this rapidly evolving field. The benchmark is publicly available at https://github.com/JoeYing1019/UltraTool.

As intelligent agents become autonomous over longer periods of time, they may eventually become lifelong counterparts to specific people. If so, it may be common for a user to want the agent to master a task temporarily but later on to forget the task due to privacy concerns. However enabling an agent to forget privately what the user specified without degrading the rest of the learned knowledge is a challenging problem. With the aim of addressing this challenge, this paper formalizes this continual learning and private unlearning (CLPU) problem. The paper further introduces a straightforward but exactly private solution, CLPU-DER++, as the first step towards solving the CLPU problem, along with a set of carefully designed benchmark problems to evaluate the effectiveness of the proposed solution. The code is available at https://github.com/Cranial-XIX/Continual-Learning-Private-Unlearning.

Foundation models have revolutionized natural language processing and artificial intelligence, significantly enhancing how machines comprehend and generate human languages. Inspired by the success of these foundation models, researchers have developed foundation models for individual scientific domains, including small molecules, materials, proteins, DNA, and RNA. However, these models are typically trained in isolation, lacking the ability to integrate across different scientific domains. Recognizing that entities within these domains can all be represented as sequences, which together form the "language of nature", we introduce Nature Language Model (briefly, NatureLM), a sequence-based science foundation model designed for scientific discovery. Pre-trained with data from multiple scientific domains, NatureLM offers a unified, versatile model that enables various applications including: (i) generating and optimizing small molecules, proteins, RNA, and materials using text instructions; (ii) cross-domain generation/design, such as protein-to-molecule and protein-to-RNA generation; and (iii) achieving state-of-the-art performance in tasks like SMILES-to-IUPAC translation and retrosynthesis on USPTO-50k. NatureLM offers a promising generalist approach for various scientific tasks, including drug discovery (hit generation/optimization, ADMET optimization, synthesis), novel material design, and the development of therapeutic proteins or nucleotides. We have developed NatureLM models in different sizes (1 billion, 8 billion, and 46.7 billion parameters) and observed a clear improvement in performance as the model size increases.

This study explores the performance of large language models (LLMs) in solving competitive programming problems from the Romanian Informatics Olympiad at the county level. Romania, a leading nation in computer science competitions, provides an ideal environment for evaluating LLM capabilities due to its rich history and stringent competition standards. We collected and analyzed a dataset comprising 304 challenges from 2002 to 2023, focusing on solutions written by LLMs in C++ and Python for these problems. Our primary goal is to understand why LLMs perform well or poorly on different tasks. We evaluated various models, including closed-source models like GPT-4 and open-weight models such as CodeLlama and RoMistral, using a standardized process involving multiple attempts and feedback rounds. The analysis revealed significant variations in LLM performance across different grades and problem types. Notably, GPT-4 showed strong performance, indicating its potential use as an educational tool for middle school students. We also observed differences in code quality and style across various LLMs

Online education platforms, leveraging the internet to distribute education resources, seek to provide convenient education but often fall short in real-time communication with students. They often struggle to offer personalized education resources due to the challenge of addressing the diverse obstacles students encounter throughout their learning journey. Recently, the emergence of large language models (LLMs), such as ChatGPT, offers the possibility for resolving this issue by comprehending individual requests. Although LLMs have been successful in various fields, creating an LLM-based education system is still challenging for the wide range of educational skills required. This paper reviews the recently emerged LLM researches related to educational capabilities, including mathematics, writing, programming, reasoning, and knowledge-based question answering, with the aim to explore their potential in constructing the next-generation intelligent education system. Based on the current development status, we further outline two approaches for an LLM-based education system: a unified approach and a mixture-of-expert (MoE) approach. Finally, we explore the challenges and future directions, providing new research opportunities and perspectives on adapting LLMs for education.

The rapid growth of Large Language Models (LLMs) has been a driving force in transforming various domains, reshaping the artificial general intelligence landscape. However, the increasing computational and memory demands of these models present substantial challenges, hindering both academic research and practical applications. To address these issues, a wide array of methods, including both algorithmic and hardware solutions, have been developed to enhance the efficiency of LLMs. This survey delivers a comprehensive review of algorithmic advancements aimed at improving LLM efficiency. Unlike other surveys that typically focus on specific areas such as training or model compression, this paper examines the multi-faceted dimensions of efficiency essential for the end-to-end algorithmic development of LLMs. Specifically, it covers various topics related to efficiency, including scaling laws, data utilization, architectural innovations, training and tuning strategies, and inference techniques. This paper aims to serve as a valuable resource for researchers and practitioners, laying the groundwork for future innovations in this critical research area. Our repository of relevant references is maintained at url{https://github.com/tding1/Efficient-LLM-Survey}.

The current evaluation of mathematical skills in LLMs is limited, as existing benchmarks are either relatively small, primarily focus on elementary and high-school problems, or lack diversity in topics. Additionally, the inclusion of visual elements in tasks remains largely under-explored. To address these gaps, we introduce U-MATH, a novel benchmark of 1,100 unpublished open-ended university-level problems sourced from teaching materials. It is balanced across six core subjects, with 20% of multimodal problems. Given the open-ended nature of U-MATH problems, we employ an LLM to judge the correctness of generated solutions. To this end, we release mu-MATH, a dataset to evaluate the LLMs' capabilities in judging solutions. The evaluation of general domain, math-specific, and multimodal LLMs highlights the challenges presented by U-MATH. Our findings reveal that LLMs achieve a maximum accuracy of only 63% on text-based tasks, with even lower 45% on visual problems. The solution assessment proves challenging for LLMs, with the best LLM judge having an F1-score of 80% on mu-MATH.

Large Language Models (LLMs) are evolving beyond their classical role of providing information within dialogue systems to actively engaging with tools and performing actions on real-world applications and services. Today, humans verify the correctness and appropriateness of the LLM-generated outputs (e.g., code, functions, or actions) before putting them into real-world execution. This poses significant challenges as code comprehension is well known to be notoriously difficult. In this paper, we study how humans can efficiently collaborate with, delegate to, and supervise autonomous LLMs in the future. We argue that in many cases, "post-facto validation" - verifying the correctness of a proposed action after seeing the output - is much easier than the aforementioned "pre-facto validation" setting. The core concept behind enabling a post-facto validation system is the integration of an intuitive undo feature, and establishing a damage confinement for the LLM-generated actions as effective strategies to mitigate the associated risks. Using this, a human can now either revert the effect of an LLM-generated output or be confident that the potential risk is bounded. We believe this is critical to unlock the potential for LLM agents to interact with applications and services with limited (post-facto) human involvement. We describe the design and implementation of our open-source runtime for executing LLM actions, Gorilla Execution Engine (GoEX), and present open research questions towards realizing the goal of LLMs and applications interacting with each other with minimal human supervision. We release GoEX at https://github.com/ShishirPatil/gorilla/.

In this paper, we introduce the Tree-of-Thought (ToT) framework, a novel approach aimed at improving the problem-solving capabilities of auto-regressive large language models (LLMs). The ToT technique is inspired by the human mind's approach for solving complex reasoning tasks through trial and error. In this process, the human mind explores the solution space through a tree-like thought process, allowing for backtracking when necessary. To implement ToT as a software system, we augment an LLM with additional modules including a prompter agent, a checker module, a memory module, and a ToT controller. In order to solve a given problem, these modules engage in a multi-round conversation with the LLM. The memory module records the conversation and state history of the problem solving process, which allows the system to backtrack to the previous steps of the thought-process and explore other directions from there. To verify the effectiveness of the proposed technique, we implemented a ToT-based solver for the Sudoku Puzzle. Experimental results show that the ToT framework can significantly increase the success rate of Sudoku puzzle solving. Our implementation of the ToT-based Sudoku solver is available on GitHub: https://github.com/jieyilong/tree-of-thought-puzzle-solver.

This paper show a work on better use of LLMs with SelfzCoT a self-prompt zero-shot CoT. Specifically, on the zero-shot arithmetic reasoning tasks, the accuracy of the proposed SelfzCoT is improved with GSM8K from 40.50% to 82.34%, with MultiArith from 79.3% to 94.7%, with ADDSUB from 74.70% to 94.10%, with SingleEq from 78.70% to 91.30%, with AQUA from 31.90% to 82.33%, and with SVAMP from 63.70% to 79.70%. Totally, using the first two lasting path activations to LLM and particularly, the code-level self-prompt, the SelfzCoT has a huge improvement on all six zero-shot arithmetic reasoning tasks. Additionally, our modified zero-shot CoT (MzCoT) also achieves remarkable performance in the reasoning tasks. The accuracy of the proposed MzCoT is enhanced with GSM8K from 40.50% to 76.32%, with MultiArith from 79.3% to 96.97%, with ADDSUB from 74.70% to 92.39%, with SingleEq from 78.70% to 94.60%, with AQUA from 31.90% to 79.90%, and with SVAMP from 63.70% to 81.50%. Notably, SelfzCoT has the best performance on GSM8K among all the recent zero-shot methods.

Software engineers working with the same programming language (PL) may speak different natural languages (NLs) and vice versa, erecting huge barriers to communication and working efficiency. Recent studies have demonstrated the effectiveness of generative pre-training in computer programs, yet they are always English-centric. In this work, we step towards bridging the gap between multilingual NLs and multilingual PLs for large language models (LLMs). We release ERNIE-Code, a unified pre-trained language model for 116 NLs and 6 PLs. We employ two methods for universal cross-lingual pre-training: span-corruption language modeling that learns patterns from monolingual NL or PL; and pivot-based translation language modeling that relies on parallel data of many NLs and PLs. Extensive results show that ERNIE-Code outperforms previous multilingual LLMs for PL or NL across a wide range of end tasks of code intelligence, including multilingual code-to-text, text-to-code, code-to-code, and text-to-text generation. We further show its advantage of zero-shot prompting on multilingual code summarization and text-to-text translation. We release our code and pre-trained checkpoints.

Given the ubiquitous nature of numbers in text, reasoning with numbers to perform simple calculations is an important skill of AI systems. While many datasets and models have been developed to this end, state-of-the-art AI systems are brittle; failing to perform the underlying mathematical reasoning when they appear in a slightly different scenario. Drawing inspiration from GLUE that was proposed in the context of natural language understanding, we propose NumGLUE, a multi-task benchmark that evaluates the performance of AI systems on eight different tasks, that at their core require simple arithmetic understanding. We show that this benchmark is far from being solved with neural models including state-of-the-art large-scale language models performing significantly worse than humans (lower by 46.4%). Further, NumGLUE promotes sharing knowledge across tasks, especially those with limited training data as evidenced by the superior performance (average gain of 3.4% on each task) when a model is jointly trained on all the tasks as opposed to task-specific modeling. Finally, we hope that NumGLUE will encourage systems that perform robust and general arithmetic reasoning within language, a first step towards being able to perform more complex mathematical reasoning.

In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance ten times more accurate than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.

Large Language Models (LLMs) have generated considerable interest and debate regarding their potential emergence of Theory of Mind (ToM). Several recent inquiries reveal a lack of robust ToM in these models and pose a pressing demand to develop new benchmarks, as current ones primarily focus on different aspects of ToM and are prone to shortcuts and data leakage. In this position paper, we seek to answer two road-blocking questions: (1) How can we taxonomize a holistic landscape of machine ToM? (2) What is a more effective evaluation protocol for machine ToM? Following psychological studies, we taxonomize machine ToM into 7 mental state categories and delineate existing benchmarks to identify under-explored aspects of ToM. We argue for a holistic and situated evaluation of ToM to break ToM into individual components and treat LLMs as an agent who is physically situated in environments and socially situated in interactions with humans. Such situated evaluation provides a more comprehensive assessment of mental states and potentially mitigates the risk of shortcuts and data leakage. We further present a pilot study in a grid world setup as a proof of concept. We hope this position paper can facilitate future research to integrate ToM with LLMs and offer an intuitive means for researchers to better position their work in the landscape of ToM. Project page: https://github.com/Mars-tin/awesome-theory-of-mind

In this technical report, we present TeleChat, a collection of large language models (LLMs) with parameters of 3 billion, 7 billion and 12 billion. It includes pretrained language models as well as fine-tuned chat models that is aligned with human preferences. TeleChat is initially pretrained on an extensive corpus containing a diverse collection of texts from both English and Chinese languages, including trillions of tokens. Subsequently, the model undergoes fine-tuning to align with human preferences, following a detailed methodology that we describe. We evaluate the performance of TeleChat on various tasks, including language understanding, mathematics, reasoning, code generation, and knowledge-based question answering. Our findings indicate that TeleChat achieves comparable performance to other open-source models of similar size across a wide range of public benchmarks. To support future research and applications utilizing LLMs, we release the fine-tuned model checkpoints of TeleChat's 7B and 12B variant, along with code and a portion of our pretraining data, to the public community.

Large Language Models for Code (Code LLM) are flourishing. New and powerful models are released on a weekly basis, demonstrating remarkable performance on the code generation task. Various approaches have been proposed to boost the code generation performance of pre-trained Code LLMs, such as supervised fine-tuning, instruction tuning, reinforcement learning, etc. In this paper, we propose a novel RRTF (Rank Responses to align Test&Teacher Feedback) framework, which can effectively and efficiently boost pre-trained large language models for code generation. Under this framework, we present PanGu-Coder2, which achieves 62.20% pass@1 on the OpenAI HumanEval benchmark. Furthermore, through an extensive evaluation on CoderEval and LeetCode benchmarks, we show that PanGu-Coder2 consistently outperforms all previous Code LLMs.

Large language models (LLMs), such as GPT-4, have shown remarkable performance in natural language processing (NLP) tasks, including challenging mathematical reasoning. However, most existing open-source models are only pre-trained on large-scale internet data and without math-related optimization. In this paper, we present WizardMath, which enhances the mathematical reasoning abilities of Llama-2, by applying our proposed Reinforcement Learning from Evol-Instruct Feedback (RLEIF) method to the domain of math. Through extensive experiments on two mathematical reasoning benchmarks, namely GSM8k and MATH, we reveal the extraordinary capabilities of our model. WizardMath surpasses all other open-source LLMs by a substantial margin. Furthermore, our model even outperforms ChatGPT-3.5, Claude Instant-1, PaLM-2 and Minerva on GSM8k, simultaneously surpasses Text-davinci-002, PaLM-1 and GPT-3 on MATH. More details and model weights are public at https://github.com/nlpxucan/WizardLM and https://huggingface.co/WizardLM.

Generative Artificial Intelligence (AI) has enabled the development of sophisticated models that are capable of producing high-caliber text, images, and other outputs through the utilization of large pre-trained models. Nevertheless, assessing the quality of the generation is an even more arduous task than the generation itself, and this issue has not been given adequate consideration recently. This paper proposes a novel evaluation framework, GPTScore, which utilizes the emergent abilities (e.g., zero-shot instruction) of generative pre-trained models to score generated texts. There are 19 pre-trained models explored in this paper, ranging in size from 80M (e.g., FLAN-T5-small) to 175B (e.g., GPT3). Experimental results on four text generation tasks, 22 evaluation aspects, and corresponding 37 datasets demonstrate that this approach can effectively allow us to achieve what one desires to evaluate for texts simply by natural language instructions. This nature helps us overcome several long-standing challenges in text evaluation--how to achieve customized, multi-faceted evaluation without the need for annotated samples. We make our code publicly available at https://github.com/jinlanfu/GPTScore.

This paper investigates the potential for large language models (LLMs) to develop private tonal languages for machine-to-machine (M2M) communication. Inspired by cryptophasia in human twins (affecting up to 50% of twin births) and natural tonal languages like Mandarin and Vietnamese, we implement a precise character-to-frequency mapping system that encodes the full ASCII character set (32-126) using musical semitones. Each character is assigned a unique frequency, creating a logarithmic progression beginning with space (220 Hz) and ending with tilde (50,175.42 Hz). This spans approximately 7.9 octaves, with higher characters deliberately mapped to ultrasonic frequencies beyond human perception (>20 kHz). Our implemented software prototype demonstrates this encoding through visualization, auditory playback, and ABC musical notation, allowing for analysis of information density and transmission speed. Testing reveals that tonal encoding can achieve information rates exceeding human speech while operating partially outside human perceptual boundaries. This work responds directly to concerns about AI systems catastrophically developing private languages within the next five years, providing a concrete prototype software example of how such communication might function and the technical foundation required for its emergence, detection, and governance.

We evaluate the reasoning abilities of large language models in multilingual settings. We introduce the Multilingual Grade School Math (MGSM) benchmark, by manually translating 250 grade-school math problems from the GSM8K dataset (Cobbe et al., 2021) into ten typologically diverse languages. We find that the ability to solve MGSM problems via chain-of-thought prompting emerges with increasing model scale, and that models have strikingly strong multilingual reasoning abilities, even in underrepresented languages such as Bengali and Swahili. Finally, we show that the multilingual reasoning abilities of language models extend to other tasks such as commonsense reasoning and word-in-context semantic judgment. The MGSM benchmark is publicly available at https://github.com/google-research/url-nlp.

In the realm of Large Language Models (LLMs), users commonly employ diverse decoding strategies and adjust hyperparameters to control the generated text. However, a critical question emerges: Are LLMs conscious of the existence of these decoding strategies and capable of regulating themselves? The current decoding generation process often relies on empirical and heuristic manual adjustments to hyperparameters based on types of tasks and demands. However, this process is typically cumbersome, and the decoding hyperparameters may not always be optimal for each sample. To address the aforementioned challenges, we propose a novel text generation paradigm termed Hyperparameter Aware Generation (HAG). By leveraging hyperparameter-aware instruction tuning, the LLM autonomously determines the optimal decoding strategy and configs based on the input samples, enabling self-regulation. Our approach eliminates the need for extensive manual tuning, offering a more autonomous, self-regulate model behavior. Experimental results spanning six datasets across reasoning, creativity, translation, and mathematics tasks demonstrate that hyperparameter-aware instruction tuning empowers the LLMs to self-regulate the decoding strategy and hyperparameter. HAG extends the current paradigm in the text generation process, highlighting the feasibility of endowing the LLMs with self-regulate decoding strategies.

One of the grand challenges of artificial general intelligence is developing agents capable of conducting scientific research and discovering new knowledge. While frontier models have already been used as aids to human scientists, e.g. for brainstorming ideas, writing code, or prediction tasks, they still conduct only a small part of the scientific process. This paper presents the first comprehensive framework for fully automatic scientific discovery, enabling frontier large language models to perform research independently and communicate their findings. We introduce The AI Scientist, which generates novel research ideas, writes code, executes experiments, visualizes results, describes its findings by writing a full scientific paper, and then runs a simulated review process for evaluation. In principle, this process can be repeated to iteratively develop ideas in an open-ended fashion, acting like the human scientific community. We demonstrate its versatility by applying it to three distinct subfields of machine learning: diffusion modeling, transformer-based language modeling, and learning dynamics. Each idea is implemented and developed into a full paper at a cost of less than $15 per paper. To evaluate the generated papers, we design and validate an automated reviewer, which we show achieves near-human performance in evaluating paper scores. The AI Scientist can produce papers that exceed the acceptance threshold at a top machine learning conference as judged by our automated reviewer. This approach signifies the beginning of a new era in scientific discovery in machine learning: bringing the transformative benefits of AI agents to the entire research process of AI itself, and taking us closer to a world where endless affordable creativity and innovation can be unleashed on the world's most challenging problems. Our code is open-sourced at https://github.com/SakanaAI/AI-Scientist

Large Language Models (LLMs) have demonstrated remarkable performance across various natural language tasks, marking significant strides towards general artificial intelligence. While general artificial intelligence is leveraged by developing increasingly large-scale models, there could be another branch to develop lightweight custom models that better serve certain domains, taking into account the high cost of training and deploying LLMs and the scarcity of resources. In this paper, we present MindLLM, a novel series of bilingual lightweight large language models, trained from scratch, alleviating such burdens by offering models with 1.3 billion and 3 billion parameters. A thorough account of experiences accrued during large model development is given, covering every step of the process, including data construction, model architecture, evaluation, and applications. Such insights are hopefully valuable for fellow academics and developers. MindLLM consistently matches or surpasses the performance of other open-source larger models on some public benchmarks. We also introduce an innovative instruction tuning framework tailored for smaller models to enhance their capabilities efficiently. Moreover, we explore the application of MindLLM in specific vertical domains such as law and finance, underscoring the agility and adaptability of our lightweight models.

The advent of large language models (LLMs) revolutionized natural language processing applications, and running LLMs on edge devices has become increasingly attractive for reasons including reduced latency, data localization, and personalized user experiences. This comprehensive review examines the challenges of deploying computationally expensive LLMs on resource-constrained devices and explores innovative solutions across multiple domains. The paper investigates the development of on-device language models, their efficient architectures, including parameter sharing and modular designs, as well as state-of-the-art compression techniques like quantization, pruning, and knowledge distillation. Hardware acceleration strategies and collaborative edge-cloud deployment approaches are analyzed, highlighting the intricate balance between performance and resource utilization. Case studies of on-device language models from major mobile manufacturers demonstrate real-world applications and potential benefits. The review also addresses critical aspects such as adaptive learning, multi-modal capabilities, and personalization. By identifying key research directions and open challenges, this paper provides a roadmap for future advancements in on-device language models, emphasizing the need for interdisciplinary efforts to realize the full potential of ubiquitous, intelligent computing while ensuring responsible and ethical deployment. For a comprehensive review of research work and educational resources on on-device large language models (LLMs), please visit https://github.com/NexaAI/Awesome-LLMs-on-device. To download and run on-device LLMs, visit https://www.nexaai.com/models.

Recent breakthroughs in large language models (LLMs) exemplified by the impressive mathematical and scientific reasoning capabilities of the o1 model have spotlighted the critical importance of high-quality training data in advancing LLM performance across STEM disciplines. While the mathematics community has benefited from a growing body of curated datasets, the scientific domain at the higher education level has long suffered from a scarcity of comparable resources. To address this gap, we present SCP-116K, a new large-scale dataset of 116,756 high-quality problem-solution pairs, automatically extracted from heterogeneous sources using a streamlined and highly generalizable pipeline. Our approach involves stringent filtering to ensure the scientific rigor and educational level of the extracted materials, while maintaining adaptability for future expansions or domain transfers. By openly releasing both the dataset and the extraction pipeline, we seek to foster research on scientific reasoning, enable comprehensive performance evaluations of new LLMs, and lower the barrier to replicating the successes of advanced models like o1 in the broader science community. We believe SCP-116K will serve as a critical resource, catalyzing progress in high-level scientific reasoning tasks and promoting further innovations in LLM development. The dataset and code are publicly available at https://github.com/AQA6666/SCP-116K-open.

Humans can learn a variety of concepts and skills incrementally over the course of their lives while exhibiting many desirable properties, such as continual learning without forgetting, forward transfer and backward transfer of knowledge, and learning a new concept or task with only a few examples. Several lines of machine learning research, such as lifelong machine learning, few-shot learning, and transfer learning attempt to capture these properties. However, most previous approaches can only demonstrate subsets of these properties, often by different complex mechanisms. In this work, we propose a simple yet powerful unified deep learning framework that supports almost all of these properties and approaches through one central mechanism. Experiments on toy examples support our claims. We also draw connections between many peculiarities of human learning (such as memory loss and "rain man") and our framework. As academics, we often lack resources required to build and train, deep neural networks with billions of parameters on hundreds of TPUs. Thus, while our framework is still conceptual, and our experiment results are surely not SOTA, we hope that this unified lifelong learning framework inspires new work towards large-scale experiments and understanding human learning in general. This paper is summarized in two short YouTube videos: https://youtu.be/gCuUyGETbTU (part 1) and https://youtu.be/XsaGI01b-1o (part 2).

We present PutnamBench, a new multilingual benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1697 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the theorems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. Proving the theorems requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.