Daily Papers

Discovering the intended items of user queries from a massive repository of items is one of the main goals of an e-commerce search system. Relevance prediction is essential to the search system since it helps improve performance. When online serving a relevance model, the model is required to perform fast and accurate inference. Currently, the widely used models such as Bi-encoder and Cross-encoder have their limitations in accuracy or inference speed respectively. In this work, we propose a novel model called the Entity-Based Relevance Model (EBRM). We identify the entities contained in an item and decompose the QI (query-item) relevance problem into multiple QE (query-entity) relevance problems; we then aggregate their results to form the QI prediction using a soft logic formulation. The decomposition allows us to use a Cross-encoder QE relevance module for high accuracy as well as cache QE predictions for fast online inference. Utilizing soft logic makes the prediction procedure interpretable and intervenable. We also show that pretraining the QE module with auto-generated QE data from user logs can further improve the overall performance. The proposed method is evaluated on labeled data from e-commerce websites. Empirical results show that it achieves promising improvements with computation efficiency.

While pre-trained language models (PLMs) are the go-to solution to tackle many natural language processing problems, they are still very limited in their ability to capture and to use common-sense knowledge. In fact, even if information is available in the form of approximate (soft) logical rules, it is not clear how to transfer it to a PLM in order to improve its performance for deductive reasoning tasks. Here, we aim to bridge this gap by teaching PLMs how to reason with soft Horn rules. We introduce a classification task where, given facts and soft rules, the PLM should return a prediction with a probability for a given hypothesis. We release the first dataset for this task, and we propose a revised loss function that enables the PLM to learn how to predict precise probabilities for the task. Our evaluation results show that the resulting fine-tuned models achieve very high performance, even on logical rules that were unseen at training. Moreover, we demonstrate that logical notions expressed by the rules are transferred to the fine-tuned model, yielding state-of-the-art results on external datasets.

A key property of reasoning systems is the ability to make sharp decisions on their input data. For contemporary AI systems, a key carrier of sharp behaviour is the softmax function, with its capability to perform differentiable query-key lookups. It is a common belief that the predictive power of networks leveraging softmax arises from "circuits" which sharply perform certain kinds of computations consistently across many diverse inputs. However, for these circuits to be robust, they would need to generalise well to arbitrary valid inputs. In this paper, we dispel this myth: even for tasks as simple as finding the maximum key, any learned circuitry must disperse as the number of items grows at test time. We attribute this to a fundamental limitation of the softmax function to robustly approximate sharp functions, prove this phenomenon theoretically, and propose adaptive temperature as an ad-hoc technique for improving the sharpness of softmax at inference time.

Modern Question Answering (QA) and Reasoning approaches based on Large Language Models (LLMs) commonly use prompting techniques, such as Chain-of-Thought (CoT), assuming the resulting generation will have a more granular exploration and reasoning over the question space and scope. However, such methods struggle with generating outputs that are faithful to the intermediate chain of reasoning produced by the model. On the other end of the spectrum, neuro-symbolic methods such as Faithful CoT (F-CoT) propose to combine LLMs with external symbolic solvers. While such approaches boast a high degree of faithfulness, they usually require a model trained for code generation and struggle with tasks that are ambiguous or hard to formalise strictly. We introduce Faithful Logic-Aided Reasoning and Exploration (\ours), a novel interpretable approach for traversing the problem space using task decompositions. We use the LLM to plan a solution, soft-formalise the query into facts and predicates using a logic programming code and simulate that code execution using an exhaustive multi-hop search over the defined space. Our method allows us to compute the faithfulness of the reasoning process w.r.t. the generated code and analyse the steps of the multi-hop search without relying on external solvers. Our methods achieve SOTA results on 7 out of 9 diverse reasoning benchmarks. We also show that model faithfulness positively correlates with overall performance and further demonstrate that {\ours} allows pinpointing the decisive factors sufficient for and leading to the correct answer with optimal reasoning during the multi-hop search.

Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of providing a system with explicit, general knowledge and having the system reason over that knowledge. However, expressing the knowledge in a formal (logical or probabilistic) representation has been a major obstacle to this research. This paper investigates a modern approach to this problem where the facts and rules are provided as natural language sentences, thus bypassing a formal representation. We train transformers to reason (or emulate reasoning) over these sentences using synthetically generated data. Our models, that we call RuleTakers, provide the first empirical demonstration that this kind of soft reasoning over language is learnable, can achieve high (99%) accuracy, and generalizes to test data requiring substantially deeper chaining than seen during training (95%+ scores). We also demonstrate that the models transfer well to two hand-authored rulebases, and to rulebases paraphrased into more natural language. These findings are significant as it suggests a new role for transformers, namely as limited "soft theorem provers" operating over explicit theories in language. This in turn suggests new possibilities for explainability, correctability, and counterfactual reasoning in question-answering.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving. Our method first utilizes LLMs to translate a natural language problem into a symbolic formulation. Afterward, a deterministic symbolic solver performs inference on the formulated problem. We also introduce a self-refinement module, which utilizes the symbolic solver's error messages to revise symbolic formalizations. We demonstrate Logic-LM's effectiveness on five logical reasoning datasets: ProofWriter, PrOntoQA, FOLIO, LogicalDeduction, and AR-LSAT. On average, Logic-LM achieves a significant performance boost of 39.2% over using LLM alone with standard prompting and 18.4% over LLM with chain-of-thought prompting. Our findings suggest that Logic-LM, by combining LLMs with symbolic logic, offers a promising avenue for faithful logical reasoning. Code and data are publicly available at https://github.com/teacherpeterpan/Logic-LLM.

Fuzzy reasoning is vital due to the frequent use of imprecise information in daily contexts. However, the ability of current large language models (LLMs) to handle such reasoning remains largely uncharted. In this paper, we introduce a new benchmark, FRoG, for fuzzy reasoning, featuring real-world mathematical word problems that incorporate generalized quantifiers. Our experimental findings reveal that fuzzy reasoning continues to pose significant challenges for LLMs. Moreover, we find that existing methods designed to enhance reasoning do not consistently improve performance in tasks involving fuzzy logic. Additionally, our results show an inverse scaling effect in the performance of LLMs on FRoG. Interestingly, we also demonstrate that strong mathematical reasoning skills are not necessarily indicative of success on our benchmark.

Extensive studies have been devoted to privatizing general-domain Large Language Models (LLMs) as Domain-Specific LLMs via feeding specific-domain data. However, these privatization efforts often ignored a critical aspect: Dual Logic Ability, which is a core reasoning ability for LLMs. The dual logic ability of LLMs ensures that they can maintain a consistent stance when confronted with both positive and negative statements about the same fact. Our study focuses on how the dual logic ability of LLMs is affected during the privatization process in the medical domain. We conduct several experiments to analyze the dual logic ability of LLMs by examining the consistency of the stance in responses to paired questions about the same fact. In our experiments, interestingly, we observed a significant decrease in the dual logic ability of existing LLMs after privatization. Besides, our results indicate that incorporating general domain dual logic data into LLMs not only enhances LLMs' dual logic ability but also further improves their accuracy. These findings underscore the importance of prioritizing LLMs' dual logic ability during the privatization process. Our study establishes a benchmark for future research aimed at exploring LLMs' dual logic ability during the privatization process and offers valuable guidance for privatization efforts in real-world applications.

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations research and mathematical optimization, which restricts non-experts' accessibility to MILP. To address this challenge, we propose a framework for automatically formulating MILP models from unstructured natural language descriptions of decision problems, which integrates Large Language Models (LLMs) and mathematical modeling techniques. This framework consists of three phases: i) identification of decision variables, ii) classification of objective and constraints, and iii) finally, generation of MILP models. In this study, we present a constraint classification scheme and a set of constraint templates that can guide the LLMs in synthesizing a complete MILP model. After fine-tuning LLMs, our approach can identify and synthesize logic constraints in addition to classic demand and resource constraints. The logic constraints have not been studied in existing work. To evaluate the performance of the proposed framework, we extend the NL4Opt dataset with more problem descriptions and constraint types, and with the new dataset, we compare our framework with one-step model generation methods offered by LLMs. The experimental results reveal that with respect to the accuracies of generating the correct model, objective, and constraints, our method which integrates constraint classification and templates with LLMs significantly outperforms the others. The prototype system that we developed has a great potential to capture more constraints for more complex MILPs. It opens up opportunities for developing training tools for operations research practitioners and has the potential to be a powerful tool for automatic decision problem modeling and solving in practice.

As a vital stage of automated rule checking (ARC), rule interpretation of regulatory texts requires considerable effort. However, interpreting regulatory clauses with implicit properties or complex computational logic is still challenging due to the lack of domain knowledge and limited expressibility of conventional logic representations. Thus, LLM-FuncMapper, an approach to identifying predefined functions needed to interpret various regulatory clauses based on the large language model (LLM), is proposed. First, by systematically analysis of building codes, a series of atomic functions are defined to capture shared computational logics of implicit properties and complex constraints, creating a database of common blocks for interpreting regulatory clauses. Then, a prompt template with the chain of thought is developed and further enhanced with a classification-based tuning strategy, to enable common LLMs for effective function identification. Finally, the proposed approach is validated with statistical analysis, experiments, and proof of concept. Statistical analysis reveals a long-tail distribution and high expressibility of the developed function database, with which almost 100% of computer-processible clauses can be interpreted and represented as computer-executable codes. Experiments show that LLM-FuncMapper achieve promising results in identifying relevant predefined functions for rule interpretation. Further proof of concept in automated rule interpretation also demonstrates the possibility of LLM-FuncMapper in interpreting complex regulatory clauses. To the best of our knowledge, this study is the first attempt to introduce LLM for understanding and interpreting complex regulatory clauses, which may shed light on further adoption of LLM in the construction domain.

The growing popularity of neuro symbolic reasoning has led to the adoption of various forms of differentiable (i.e., fuzzy) first order logic. We introduce PyReason, a software framework based on generalized annotated logic that both captures the current cohort of differentiable logics and temporal extensions to support inference over finite periods of time with capabilities for open world reasoning. Further, PyReason is implemented to directly support reasoning over graphical structures (e.g., knowledge graphs, social networks, biological networks, etc.), produces fully explainable traces of inference, and includes various practical features such as type checking and a memory-efficient implementation. This paper reviews various extensions of generalized annotated logic integrated into our implementation, our modern, efficient Python-based implementation that conducts exact yet scalable deductive inference, and a suite of experiments. PyReason is available at: github.com/lab-v2/pyreason.

Softmax attention is the principle backbone of foundation models for various artificial intelligence applications, yet its quadratic complexity in sequence length can limit its inference throughput in long-context settings. To address this challenge, alternative architectures such as linear attention, State Space Models (SSMs), and Recurrent Neural Networks (RNNs) have been considered as more efficient alternatives. While connections between these approaches exist, such models are commonly developed in isolation and there is a lack of theoretical understanding of the shared principles underpinning these architectures and their subtle differences, greatly influencing performance and scalability. In this paper, we introduce the Dynamical Systems Framework (DSF), which allows a principled investigation of all these architectures in a common representation. Our framework facilitates rigorous comparisons, providing new insights on the distinctive characteristics of each model class. For instance, we compare linear attention and selective SSMs, detailing their differences and conditions under which both are equivalent. We also provide principled comparisons between softmax attention and other model classes, discussing the theoretical conditions under which softmax attention can be approximated. Additionally, we substantiate these new insights with empirical validations and mathematical arguments. This shows the DSF's potential to guide the systematic development of future more efficient and scalable foundation models.

In this thesis, I evaluate the performance of Large Language Models (LLMs) on the Law School Admissions Test (LSAT), specifically the Logic Games section of the test. I focus on this section because it presents a complex logical reasoning task and thus is a valuable source of data for evaluating how modern, increasingly capable LLMs can handle hard logical reasoning tasks. I construct a dataset of LSAT logic games and their associated metadata, and extensively evaluate LLMs' performance in a Chain-of-Thought prompting setting. Given the weak performance in this setting, I explore other prompting frameworks on a smaller subset of the dataset, adapting ideas from Reflexion to this task. This results in a substantially improved accuracy of 70 percent for GPT-4 and 46 percent for GPT-3.5 on this data subset, highlighting the capacity of LLMs to revise their logical errors, despite initially weak performance. Finally, I analyze the types of logic games that models perform better or worse on, as well as the types of logical errors I observe from human annotation, providing detailed insights on the logical reasoning capabilities of LLMs.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

Game theory is a powerful framework for reasoning about strategic interactions, with applications in domains ranging from day-to-day life to international politics. However, applying formal reasoning tools in such contexts is challenging, as these scenarios are often expressed in natural language. To address this, we introduce a framework for the autoformalization of game-theoretic scenarios, which translates natural language descriptions into formal logic representations suitable for formal solvers. Our approach utilizes one-shot prompting and a solver that provides feedback on syntactic correctness to allow LLMs to refine the code. We evaluate the framework using GPT-4o and a dataset of natural language problem descriptions, achieving 98% syntactic correctness and 88% semantic correctness. These results show the potential of LLMs to bridge the gap between real-life strategic interactions and formal reasoning.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Divergent thinking, the cognitive process of generating diverse solutions, is a hallmark of human creativity and problem-solving. For machines, sampling diverse solution trajectories in complex reasoning problems is crucial for robust outcomes, data augmentation, and enhanced model generalization. Large language models (LLMs) often struggle with generating high-quality, diverse reasoning. While supervised fine-tuning helps with quality, it requires extensive supervision data to capture the full diversity of solutions. Alternatively, reinforcement learning methods like PPO aim to find limited highest-reward solutions while neglecting the solution diversity, akin to convergent thinking. To address these limitations, we propose Flow of Reasoning (FoR) -- an efficient LLM training approach enabling diverse reasoning with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow from an initial state to terminal states. The formulation allows to adapt principled GFlowNet approaches to train the LLM as a policy, which is able to sample multiple reasoning paths with probabilities proportional to the unnormalized reward. Empirical results show that, with limited training data (e.g., 15 examples), FoR can discover diverse high-quality solutions that excel greatly beyond current state-of-the-art methods across three tasks, including embodied reasoning (BlocksWorld), math puzzle solving (Game24), and logical reasoning (PrOntoQA). Code is available at https://github.com/Yu-Fangxu/FoR.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-V3, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending large language models (LLMs) with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining Reinforcement Learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), and supervision schemes (Output-Based and Process-Based Supervision). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we outline how RLMs can integrate with a broader LLM ecosystem, including tools and databases. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM development and experimentation.

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of LLMs. To address this, our goals are to make model beliefs and their inferential relationships explicit, and to resolve inconsistencies that may exist, so that answers are supported by interpretable chains of reasoning drawn from a consistent network of beliefs. Our approach, which we call REFLEX, is to add a rational, self-reflecting layer on top of the LLM. First, given a question, we construct a belief graph using a backward-chaining process to materialize relevant model beliefs (including beliefs about answer candidates) and their inferential relationships. Second, we identify and minimize contradictions in that graph using a formal constraint reasoner. We find that REFLEX significantly improves consistency (by 8%-11% absolute) without harming overall answer accuracy, resulting in answers supported by faithful chains of reasoning drawn from a more consistent belief system. This suggests a new style of system architecture in which an LLM extended with a rational layer can provide an interpretable window into system beliefs, add a systematic reasoning capability, and repair latent inconsistencies present in the LLM.

Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to reason abilities for generalization and composition. Recently, the prevailing method is query embedding which learns the embedding of a set of entities and treats logic operations as set operations and has shown great empirical success. Though there has been much research following the same formulation, many of its claims lack a formal and systematic inspection. In this paper, we rethink this formulation and justify many of the previous claims by characterizing the scope of queries investigated previously and precisely identifying the gap between its formulation and its goal, as well as providing complexity analysis for the currently investigated queries. Moreover, we develop a new dataset containing ten new types of queries with features that have never been considered and therefore can provide a thorough investigation of complex queries. Finally, we propose a new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where we equip the neural link predictors with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability. Empirical results show that our method outperforms previous methods significantly in the new dataset and also surpasses previous methods in the existing dataset at the same time.

Despite their linguistic competence, Large Language models (LLMs) often exhibit limitations in their ability to reason reliably and flexibly. To address this, we propose a neurosymbolic approach that prompts LLMs to extract and encode all relevant information from a problem statement as logical code statements, and then use a logic programming language (Prolog) to conduct the iterative computations of explicit deductive reasoning. Our approach significantly enhances the performance of LLMs on the standard mathematical reasoning benchmark, GSM8k, and the Navigate dataset from the BIG-bench dataset. Additionally, we introduce a novel dataset, the Non-Linear Reasoning (NLR) dataset, consisting of 55 unique word problems that target the shortcomings of the next token prediction paradigm of LLMs and require complex non-linear reasoning but only basic arithmetic skills to solve. Our findings demonstrate that the integration of Prolog enables LLMs to achieve high performance on the NLR dataset, which even the most advanced language models (including GPT4) fail to solve using text only.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

Large language models (LLMs) such as ChatGPT have recently demonstrated significant potential in mathematical abilities, providing valuable reasoning paradigm consistent with human natural language. However, LLMs currently have difficulty in bridging perception, language understanding and reasoning capabilities due to incompatibility of the underlying information flow among them, making it challenging to accomplish tasks autonomously. On the other hand, abductive learning (ABL) frameworks for integrating the two abilities of perception and reasoning has seen significant success in inverse decipherment of incomplete facts, but it is limited by the lack of semantic understanding of logical reasoning rules and the dependence on complicated domain knowledge representation. This paper presents a novel method (ChatABL) for integrating LLMs into the ABL framework, aiming at unifying the three abilities in a more user-friendly and understandable manner. The proposed method uses the strengths of LLMs' understanding and logical reasoning to correct the incomplete logical facts for optimizing the performance of perceptual module, by summarizing and reorganizing reasoning rules represented in natural language format. Similarly, perceptual module provides necessary reasoning examples for LLMs in natural language format. The variable-length handwritten equation deciphering task, an abstract expression of the Mayan calendar decoding, is used as a testbed to demonstrate that ChatABL has reasoning ability beyond most existing state-of-the-art methods, which has been well supported by comparative studies. To our best knowledge, the proposed ChatABL is the first attempt to explore a new pattern for further approaching human-level cognitive ability via natural language interaction with ChatGPT.

Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies on logical reasoning. Large Language Models (LLMs) attempt to emulate human language understanding and generation, but their competency in logical reasoning remains limited. This paper seeks to address the philosophical question: How can we effectively teach logical reasoning to LLMs while maintaining a deep understanding of the intricate relationship between language and logic? By focusing on bolstering LLMs' capabilities in logical reasoning, we aim to expand their applicability in law and other logic-intensive disciplines. To this end, we propose a Reinforcement Learning from Logical Feedback (RLLF) approach, which serves as a potential framework for refining LLMs' reasoning capacities. Through RLLF and a revised evaluation methodology, we explore new avenues for research in this domain and contribute to the development of LLMs capable of handling complex legal reasoning tasks while acknowledging the fundamental connection between language and logic.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

This survey paper proposes a clearer view of natural language reasoning in the field of Natural Language Processing (NLP), both conceptually and practically. Conceptually, we provide a distinct definition for natural language reasoning in NLP, based on both philosophy and NLP scenarios, discuss what types of tasks require reasoning, and introduce a taxonomy of reasoning. Practically, we conduct a comprehensive literature review on natural language reasoning in NLP, mainly covering classical logical reasoning, natural language inference, multi-hop question answering, and commonsense reasoning. The paper also identifies and views backward reasoning, a powerful paradigm for multi-step reasoning, and introduces defeasible reasoning as one of the most important future directions in natural language reasoning research. We focus on single-modality unstructured natural language text, excluding neuro-symbolic techniques and mathematical reasoning.

While large language models (LLMs) equipped with techniques like chain-of-thought prompting have demonstrated impressive capabilities, they still fall short in their ability to reason robustly in complex settings. However, evaluating LLM reasoning is challenging because system capabilities continue to grow while benchmark datasets for tasks like logical deduction have remained static. We introduce MuSR, a dataset for evaluating language models on multistep soft reasoning tasks specified in a natural language narrative. This dataset has two crucial features. First, it is created through a novel neurosymbolic synthetic-to-natural generation algorithm, enabling the construction of complex reasoning instances that challenge GPT-4 (e.g., murder mysteries roughly 1000 words in length) and which can be scaled further as more capable LLMs are released. Second, our dataset instances are free text narratives corresponding to real-world domains of reasoning; this makes it simultaneously much more challenging than other synthetically-crafted benchmarks while remaining realistic and tractable for human annotators to solve with high accuracy. We evaluate a range of LLMs and prompting techniques on this dataset and characterize the gaps that remain for techniques like chain-of-thought to perform robust reasoning.

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Despite their tremendous success in many applications, large language models often fall short of consistent reasoning and planning in various (language, embodied, and social) scenarios, due to inherent limitations in their inference, learning, and modeling capabilities. In this position paper, we present a new perspective of machine reasoning, LAW, that connects the concepts of Language models, Agent models, and World models, for more robust and versatile reasoning capabilities. In particular, we propose that world and agent models are a better abstraction of reasoning, that introduces the crucial elements of deliberate human-like reasoning, including beliefs about the world and other agents, anticipation of consequences, goals/rewards, and strategic planning. Crucially, language models in LAW serve as a backend to implement the system or its elements and hence provide the computational power and adaptability. We review the recent studies that have made relevant progress and discuss future research directions towards operationalizing the LAW framework.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Large language models (LLMs) are powerful AI tools that can generate and comprehend natural language text and other complex information. However, the field lacks a mathematical framework to systematically describe, compare and improve LLMs. We propose Hex a framework that clarifies key terms and concepts in LLM research, such as hallucinations, alignment, self-verification and chain-of-thought reasoning. The Hex framework offers a precise and consistent way to characterize LLMs, identify their strengths and weaknesses, and integrate new findings. Using Hex, we differentiate chain-of-thought reasoning from chain-of-thought prompting and establish the conditions under which they are equivalent. This distinction clarifies the basic assumptions behind chain-of-thought prompting and its implications for methods that use it, such as self-verification and prompt programming. Our goal is to provide a formal framework for LLMs that can help both researchers and practitioners explore new possibilities for generative AI. We do not claim to have a definitive solution, but rather a tool for opening up new research avenues. We argue that our formal definitions and results are crucial for advancing the discussion on how to build generative AI systems that are safe, reliable, fair and robust, especially in domains like healthcare and software engineering.

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and others parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Large Language Models have been shown to fail to create executable and verifiable plans in grounded environments. An emerging line of work shows success in using LLM as a formalizer to generate a formal representation (e.g., PDDL) of the planning domain, which can be deterministically solved to find a plan. We systematically evaluate this methodology while bridging some major gaps. While previous work only generates a partial PDDL representation given templated and thus unrealistic environment descriptions, we generate the complete representation given descriptions of various naturalness levels. Among an array of observations critical to improve LLMs' formal planning ability, we note that large enough models can effectively formalize descriptions as PDDL, outperforming those directly generating plans, while being robust to lexical perturbation. As the descriptions become more natural-sounding, we observe a decrease in performance and provide detailed error analysis.

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

It has been well-known that Chain-of-Thought can remarkably enhance LLMs' performance on complex tasks. However, because it also introduces slower inference speeds and higher computational costs, many researches have attempted to use implicit CoT, which does not need LLMs to explicitly generate the intermediate steps. But there is still gap between their efficacy and typical explicit CoT methods. This leaves us a doubt that, does implicit CoT really equal to explicit CoT? Therefore, in this study, we address this question through experiments. We probe the information of intermediate steps from the model's hidden states when it is performing implicit CoT. The results surprisingly indicate that LLMs hardly think about intermediate steps, suggesting they may just rely on experience rather than strict step-by-step reasoning. Moreover, we find LLMs' implicit reasoning capabilities are susceptible and unstable, reaffirming the necessity of explicit CoT to effectively support complex tasks.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary, limiting the generalizability of acquired reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. Then, using the proposed corpora, which we name FLD (Formal Logic Deduction), we first evaluate and analyze the logical reasoning ability of the latest LLMs. Even GPT-4 can solve only half of the problems, suggesting that pure logical reasoning isolated from knowledge is still challenging for the LLMs, and additional training specialized in logical reasoning is indeed essential. We next empirically verify that LMs trained on FLD corpora acquire more generalizable reasoning ability. Furthermore, we identify the aspects of reasoning ability on which deduction corpora can enhance LMs and those on which they cannot, and discuss future directions on each aspect. The released corpora serve both as learning resources and as challenging benchmarks.

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing benchmarks often rely on extensive human annotation or handcrafted templates, making it difficult to achieve the necessary complexity, scalability, and diversity for robust evaluation. To address these limitations, we propose a novel framework called ProverGen that synergizes the generative strengths of Large Language Models (LLMs) with the rigor and precision of symbolic provers, enabling the creation of a scalable, diverse, and high-quality FOL reasoning dataset, ProverQA. ProverQA is also distinguished by its inclusion of accessible and logically coherent intermediate reasoning steps for each problem. Our evaluation shows that state-of-the-art LLMs struggle to solve ProverQA problems, even with CoT prompting, highlighting the dataset's challenging nature. We also finetune Llama3.1-8B-Instruct on a separate training set generated by our framework. The finetuned model demonstrates consistent improvements on both in-distribution and out-of-distribution test sets, suggesting the value of our proposed data generation framework. Code available at: https://github.com/opendatalab/ProverGen

Large Language Models (LLMs) have shown impressive performance in complex reasoning tasks through Chain-of-Thought (CoT) reasoning, allowing models to break down problems into manageable sub-tasks. However, existing CoT evaluation techniques either require annotated CoT data or fall short in accurately assessing intermediate reasoning steps, leading to high rates of false positives. In this paper, we formalize CoT reasoning in LLMs through an information-theoretic lens. Specifically, our framework quantifies the `information gain' at each reasoning step, enabling the identification of failure modes in LLMs without the need for expensive annotated datasets. We demonstrate the efficacy of our approach through extensive experiments on toy and GSM-8K data, where it significantly outperforms existing outcome-based methods by providing more accurate insights into model performance on individual tasks.

Large language models (LLMs) have dramatically enhanced the field of language intelligence, as demonstrably evidenced by their formidable empirical performance across a spectrum of complex reasoning tasks. Additionally, theoretical proofs have illuminated their emergent reasoning capabilities, providing a compelling showcase of their advanced cognitive abilities in linguistic contexts. Critical to their remarkable efficacy in handling complex reasoning tasks, LLMs leverage the intriguing chain-of-thought (CoT) reasoning techniques, obliging them to formulate intermediate steps en route to deriving an answer. The CoT reasoning approach has not only exhibited proficiency in amplifying reasoning performance but also in enhancing interpretability, controllability, and flexibility. In light of these merits, recent research endeavors have extended CoT reasoning methodologies to nurture the development of autonomous language agents, which adeptly adhere to language instructions and execute actions within varied environments. This survey paper orchestrates a thorough discourse, penetrating vital research dimensions, encompassing: (i) the foundational mechanics of CoT techniques, with a focus on elucidating the circumstances and justification behind its efficacy; (ii) the paradigm shift in CoT; and (iii) the burgeoning of language agents fortified by CoT approaches. Prospective research avenues envelop explorations into generalization, efficiency, customization, scaling, and safety. This paper caters to a wide audience, including beginners seeking comprehensive knowledge of CoT reasoning and language agents, as well as experienced researchers interested in foundational mechanics and engaging in cutting-edge discussions on these topics. A repository for the related papers is available at https://github.com/Zoeyyao27/CoT-Igniting-Agent.

Generalized quantifiers (e.g., few, most) are used to indicate the proportions predicates are satisfied (for example, some apples are red). One way to interpret quantifier semantics is to explicitly bind these satisfactions with percentage scopes (e.g., 30%-40% of apples are red). This approach can be helpful for tasks like logic formalization and surface-form quantitative reasoning (Gordon and Schubert, 2010; Roy et al., 2015). However, it remains unclear if recent foundation models possess this ability, as they lack direct training signals. To explore this, we introduce QuRe, a crowd-sourced dataset of human-annotated generalized quantifiers in Wikipedia sentences featuring percentage-equipped predicates. We explore quantifier comprehension in language models using PRESQUE, a framework that combines natural language inference and the Rational Speech Acts framework. Experimental results on the HVD dataset and QuRe illustrate that PRESQUE, employing pragmatic reasoning, performs 20% better than a literal reasoning baseline when predicting quantifier percentage scopes, with no additional training required.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

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.

Logical rules are essential for uncovering the logical connections between relations, which could improve the reasoning performance and provide interpretable results on knowledge graphs (KGs). Although there have been many efforts to mine meaningful logical rules over KGs, existing methods suffer from the computationally intensive searches over the rule space and a lack of scalability for large-scale KGs. Besides, they often ignore the semantics of relations which is crucial for uncovering logical connections. Recently, large language models (LLMs) have shown impressive performance in the field of natural language processing and various applications, owing to their emergent ability and generalizability. In this paper, we propose a novel framework, ChatRule, unleashing the power of large language models for mining logical rules over knowledge graphs. Specifically, the framework is initiated with an LLM-based rule generator, leveraging both the semantic and structural information of KGs to prompt LLMs to generate logical rules. To refine the generated rules, a rule ranking module estimates the rule quality by incorporating facts from existing KGs. Last, a rule validator harnesses the reasoning ability of LLMs to validate the logical correctness of ranked rules through chain-of-thought reasoning. ChatRule is evaluated on four large-scale KGs, w.r.t. different rule quality metrics and downstream tasks, showing the effectiveness and scalability of our method.

Large Language Models have shown tremendous performance on a large variety of natural language processing tasks, ranging from text comprehension to common sense reasoning. However, the mechanisms responsible for this success remain opaque, and it is unclear whether LLMs can achieve human-like cognitive capabilities or whether these models are still fundamentally circumscribed. Abstract reasoning is a fundamental task for cognition, consisting of finding and applying a general pattern from few data. Evaluating deep neural architectures on this task could give insight into their potential limitations regarding reasoning and their broad generalisation abilities, yet this is currently an under-explored area. In this paper, we introduce a new benchmark for evaluating language models beyond memorization on abstract reasoning tasks. We perform extensive evaluations of state-of-the-art LLMs, showing that they currently achieve very limited performance in contrast with other natural language tasks, and we examine the reasons for this difference. We apply techniques that have been shown to improve performance on other NLP tasks and show that their impact on abstract reasoning is limited.

A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software systems, is reviewed at a moderate level of detail. The review covers underlying philosophies (patternist philosophy of mind, foundational phenomenological and logical ontology), formalizations of the concept of intelligence, and a proposed high level architecture for AGI systems partly driven by these formalizations and philosophies. The implementation of specific cognitive processes such as logical reasoning, program learning, clustering and attention allocation in the context and language of this high level architecture is considered, as is the importance of a common (e.g. typed metagraph based) knowledge representation for enabling "cognitive synergy" between the various processes. The specifics of human-like cognitive architecture are presented as manifestations of these general principles, and key aspects of machine consciousness and machine ethics are also treated in this context. Lessons for practical implementation of advanced AGI in frameworks such as OpenCog Hyperon are briefly considered.

We propose DISC-LawLLM, an intelligent legal system utilizing large language models (LLMs) to provide a wide range of legal services. We adopt legal syllogism prompting strategies to construct supervised fine-tuning datasets in the Chinese Judicial domain and fine-tune LLMs with legal reasoning capability. We augment LLMs with a retrieval module to enhance models' ability to access and utilize external legal knowledge. A comprehensive legal benchmark, DISC-Law-Eval, is presented to evaluate intelligent legal systems from both objective and subjective dimensions. Quantitative and qualitative results on DISC-Law-Eval demonstrate the effectiveness of our system in serving various users across diverse legal scenarios. The detailed resources are available at https://github.com/FudanDISC/DISC-LawLLM.

Multimodal Large Language Model (MLLM) recently has been a new rising research hotspot, which uses powerful Large Language Models (LLMs) as a brain to perform multimodal tasks. The surprising emergent capabilities of MLLM, such as writing stories based on images and OCR-free math reasoning, are rare in traditional methods, suggesting a potential path to artificial general intelligence. In this paper, we aim to trace and summarize the recent progress of MLLM. First of all, we present the formulation of MLLM and delineate its related concepts. Then, we discuss the key techniques and applications, including Multimodal Instruction Tuning (M-IT), Multimodal In-Context Learning (M-ICL), Multimodal Chain of Thought (M-CoT), and LLM-Aided Visual Reasoning (LAVR). Finally, we discuss existing challenges and point out promising research directions. In light of the fact that the era of MLLM has only just begun, we will keep updating this survey and hope it can inspire more research. An associated GitHub link collecting the latest papers is available at https://github.com/BradyFU/Awesome-Multimodal-Large-Language-Models.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

Reasoning has long been viewed as an emergent property of large language models (LLMs), appearing at or above a certain scale (sim100B parameters). However, recent studies challenge this assumption, showing that small language models (SLMs) can also achieve competitive reasoning performance. SLMs are increasingly favored for their efficiency and deployability. However, there is a lack of systematic study on the reasoning abilities of diverse SLMs, including those trained from scratch or derived from LLMs through quantization, pruning, and distillation. This raises a critical question: Can SLMs achieve reasoning abilities comparable to LLMs? In this work, we systematically survey, benchmark, and analyze 72 SLMs from six model families across 14 reasoning benchmarks. For reliable evaluation, we examine four evaluation methods and compare four LLM judges against human evaluations on 800 data points. We repeat all experiments three times to ensure a robust performance assessment. Additionally, we analyze the impact of different prompting strategies in small models. Beyond accuracy, we also evaluate model robustness under adversarial conditions and intermediate reasoning steps. Our findings challenge the assumption that scaling is the only way to achieve strong reasoning. Instead, we foresee a future where SLMs with strong reasoning capabilities can be developed through structured training or post-training compression. They can serve as efficient alternatives to LLMs for reasoning-intensive tasks.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

Strong Artificial Intelligence (Strong AI) or Artificial General Intelligence (AGI) with abstract reasoning ability is the goal of next-generation AI. Recent advancements in Large Language Models (LLMs), along with the emerging field of Multimodal Large Language Models (MLLMs), have demonstrated impressive capabilities across a wide range of multimodal tasks and applications. Particularly, various MLLMs, each with distinct model architectures, training data, and training stages, have been evaluated across a broad range of MLLM benchmarks. These studies have, to varying degrees, revealed different aspects of the current capabilities of MLLMs. However, the reasoning abilities of MLLMs have not been systematically investigated. In this survey, we comprehensively review the existing evaluation protocols of multimodal reasoning, categorize and illustrate the frontiers of MLLMs, introduce recent trends in applications of MLLMs on reasoning-intensive tasks, and finally discuss current practices and future directions. We believe our survey establishes a solid base and sheds light on this important topic, multimodal reasoning.

While Large Language Models (LLMs) have demonstrated their proficiency in complex reasoning tasks, their performance in dynamic, interactive, and competitive scenarios - such as business strategy and stock market analysis - remains underexplored. To bridge this gap, we formally explore the dynamic reasoning capabilities of LLMs for decision-making in rapidly evolving environments. We introduce two game theory-based pilot challenges that mirror the complexities of real-world dynamic decision-making. These challenges are well-defined, enabling clear, controllable, and precise evaluation of LLMs' dynamic reasoning abilities. Through extensive experiments, we find that existing reasoning methods tend to falter in dynamic settings that require k-level thinking - a key concept not tackled by previous works. To address this, we propose a novel reasoning approach for LLMs, named "K-Level Reasoning". This approach adopts the perspective of rivals to recursively employ k-level thinking based on available historical information, which significantly improves the prediction accuracy of rivals' subsequent moves and informs more strategic decision-making. This research not only sets a robust quantitative benchmark for the assessment of dynamic reasoning but also markedly enhances the proficiency of LLMs in dynamic contexts.

While LLMs can provide reasoned explanations along with their answers, the nature and quality of those explanations are still poorly understood. In response, our goal is to define a detailed way of characterizing the explanation capabilities of modern models and to create a nuanced, interpretable explanation evaluation tool that can generate such characterizations automatically, without relying on expensive API calls or human annotations. Our approach is to (a) define the new task of explanation critiquing - identifying and categorizing any main flaw in an explanation and providing suggestions to address the flaw, (b) create a sizeable, human-verified dataset for this task, and (c) train an open-source, automatic critiquing model (called Digital Socrates) using this data. Through quantitative and qualitative analysis, we demonstrate how Digital Socrates is useful for revealing insights about student models by examining their reasoning chains, and how it can provide high-quality, nuanced, automatic evaluation of those model explanations for the first time. Digital Socrates thus fills an important gap in evaluation tools for understanding and improving the explanation behavior of models.

Large Language Models (LLMs) have demonstrated notable capabilities across various tasks, showcasing complex problem-solving abilities. Understanding and executing complex rules, along with multi-step planning, are fundamental to logical reasoning and critical for practical LLM agents and decision-making systems. However, evaluating LLMs as effective rule-based executors and planners remains underexplored. In this paper, we introduce LogicGame, a novel benchmark designed to evaluate the comprehensive rule understanding, execution, and planning capabilities of LLMs. Unlike traditional benchmarks, LogicGame provides diverse games that contain a series of rules with an initial state, requiring models to comprehend and apply predefined regulations to solve problems. We create simulated scenarios in which models execute or plan operations to achieve specific outcomes. These game scenarios are specifically designed to distinguish logical reasoning from mere knowledge by relying exclusively on predefined rules. This separation allows for a pure assessment of rule-based reasoning capabilities. The evaluation considers not only final outcomes but also intermediate steps, providing a comprehensive assessment of model performance. Moreover, these intermediate steps are deterministic and can be automatically verified. LogicGame defines game scenarios with varying difficulty levels, from simple rule applications to complex reasoning chains, in order to offer a precise evaluation of model performance on rule understanding and multi-step execution. Utilizing LogicGame, we test various LLMs and identify notable shortcomings in their rule-based logical reasoning abilities.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between inductive and deductive reasoning, leading to a blending of the two. This raises an essential question: In LLM reasoning, which poses a greater challenge - deductive or inductive reasoning? While the deductive reasoning capabilities of LLMs, (i.e. their capacity to follow instructions in reasoning tasks), have received considerable attention, their abilities in true inductive reasoning remain largely unexplored. To investigate into the true inductive reasoning capabilities of LLMs, we propose a novel framework, SolverLearner. This framework enables LLMs to learn the underlying function (i.e., y = f_w(x)), that maps input data points (x) to their corresponding output values (y), using only in-context examples. By focusing on inductive reasoning and separating it from LLM-based deductive reasoning, we can isolate and investigate inductive reasoning of LLMs in its pure form via SolverLearner. Our observations reveal that LLMs demonstrate remarkable inductive reasoning capabilities through SolverLearner, achieving near-perfect performance with ACC of 1 in most cases. Surprisingly, despite their strong inductive reasoning abilities, LLMs tend to relatively lack deductive reasoning capabilities, particularly in tasks involving ``counterfactual'' reasoning.

Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning about group polarization using logical systems. In this work we consider the modal logic PNL that captures the notion of agents agreeing or disagreeing on a given topic. Our contribution involves enhancing PNL with advanced formal reasoning techniques, instead of relying on axiomatic systems for analyzing group polarization. To achieve this, we introduce a semantic game tailored for (hybrid) extensions of PNL. This game fosters dynamic reasoning about concrete network models, aligning with our goal of strengthening PNL's effectiveness in studying group polarization. We show how this semantic game leads to a provability game by systemically exploring the truth in all models. This leads to the first cut-free sequent systems for some variants of PNL. Using polarization of formulas, the proposed calculi can be modularly adapted to consider different frame properties of the underlying model.

Distilling knowledge from a large teacher model to a lightweight one is a widely successful approach for generating compact, powerful models in the semi-supervised learning setting where a limited amount of labeled data is available. In large-scale applications, however, the teacher tends to provide a large number of incorrect soft-labels that impairs student performance. The sheer size of the teacher additionally constrains the number of soft-labels that can be queried due to prohibitive computational and/or financial costs. The difficulty in achieving simultaneous efficiency (i.e., minimizing soft-label queries) and robustness (i.e., avoiding student inaccuracies due to incorrect labels) hurts the widespread application of knowledge distillation to many modern tasks. In this paper, we present a parameter-free approach with provable guarantees to query the soft-labels of points that are simultaneously informative and correctly labeled by the teacher. At the core of our work lies a game-theoretic formulation that explicitly considers the inherent trade-off between the informativeness and correctness of input instances. We establish bounds on the expected performance of our approach that hold even in worst-case distillation instances. We present empirical evaluations on popular benchmarks that demonstrate the improved distillation performance enabled by our work relative to that of state-of-the-art active learning and active distillation methods.

The emergent few-shot reasoning capabilities of Large Language Models (LLMs) have excited the natural language and machine learning community over recent years. Despite of numerous successful applications, the underlying mechanism of such in-context capabilities still remains unclear. In this work, we hypothesize that the learned semantics of language tokens do the most heavy lifting during the reasoning process. Different from human's symbolic reasoning process, the semantic representations of LLMs could create strong connections among tokens, thus composing a superficial logical chain. To test our hypothesis, we decouple semantics from the language reasoning process and evaluate three kinds of reasoning abilities, i.e., deduction, induction and abduction. Our findings reveal that semantics play a vital role in LLMs' in-context reasoning -- LLMs perform significantly better when semantics are consistent with commonsense but struggle to solve symbolic or counter-commonsense reasoning tasks by leveraging in-context new knowledge. The surprising observations question whether modern LLMs have mastered the inductive, deductive and abductive reasoning abilities as in human intelligence, and motivate research on unveiling the magic existing within the black-box LLMs. On the whole, our analysis provides a novel perspective on the role of semantics in developing and evaluating language models' reasoning abilities. Code is available at {https://github.com/XiaojuanTang/ICSR}.

Recently, slow-thinking reasoning systems, built upon large language models (LLMs), have garnered widespread attention by scaling the thinking time during inference. There is also growing interest in adapting this capability to multimodal large language models (MLLMs). Given that MLLMs handle more complex data semantics across different modalities, it is intuitively more challenging to implement multimodal slow-thinking systems. To address this issue, in this paper, we explore a straightforward approach by fine-tuning a capable MLLM with a small amount of textual long-form thought data, resulting in a multimodal slow-thinking system, Virgo (Visual reasoning with long thought). We find that these long-form reasoning processes, expressed in natural language, can be effectively transferred to MLLMs. Moreover, it seems that such textual reasoning data can be even more effective than visual reasoning data in eliciting the slow-thinking capacities of MLLMs. While this work is preliminary, it demonstrates that slow-thinking capacities are fundamentally associated with the language model component, which can be transferred across modalities or domains. This finding can be leveraged to guide the development of more powerful slow-thinking reasoning systems. We release our resources at https://github.com/RUCAIBox/Virgo.

We examine how well the state-of-the-art (SOTA) models used in legal reasoning support abductive reasoning tasks. Abductive reasoning is a form of logical inference in which a hypothesis is formulated from a set of observations, and that hypothesis is used to explain the observations. The ability to formulate such hypotheses is important for lawyers and legal scholars as it helps them articulate logical arguments, interpret laws, and develop legal theories. Our motivation is to consider the belief that deep learning models, especially large language models (LLMs), will soon replace lawyers because they perform well on tasks related to legal text processing. But to do so, we believe, requires some form of abductive hypothesis formation. In other words, while LLMs become more popular and powerful, we want to investigate their capacity for abductive reasoning. To pursue this goal, we start by building a logic-augmented dataset for abductive reasoning with 498,697 samples and then use it to evaluate the performance of a SOTA model in the legal field. Our experimental results show that although these models can perform well on tasks related to some aspects of legal text processing, they still fall short in supporting abductive reasoning tasks.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

Large language models (LLMs) exhibit impressive emergent abilities in natural language processing, but their democratization is hindered due to huge computation requirements and closed-source nature. Recent research on advancing open-source smaller LMs by distilling knowledge from black-box LLMs has obtained promising results in the instruction-following ability. However, the reasoning ability which is more challenging to foster, is relatively rarely explored. In this paper, we propose a tailored learning approach to distill such reasoning ability to smaller LMs to facilitate the democratization of the exclusive reasoning ability. In contrast to merely employing LLM as a data annotator, we exploit the potential of LLM as a reasoning teacher by building an interactive multi-round learning paradigm. This paradigm enables the student to expose its deficiencies to the black-box teacher who then can provide customized training data in return. Further, to exploit the reasoning potential of the smaller LM, we propose self-reflection learning to motivate the student to learn from self-made mistakes. The learning from self-reflection and LLM are all tailored to the student's learning status, thanks to the seamless integration with the multi-round learning paradigm. Comprehensive experiments and analysis on mathematical and commonsense reasoning tasks demonstrate the effectiveness of our method. The code will be available at https://github.com/Raibows/Learn-to-Reason.

As large language models (LLMs) are continuously being developed, their evaluation becomes increasingly important yet challenging. This work proposes Chain-of-Thought Hub, an open-source evaluation suite on the multi-step reasoning capabilities of large language models. We are interested in this setting for two reasons: (1) from the behavior of GPT and PaLM model family, we observe that complex reasoning is likely to be a key differentiator between weaker and stronger LLMs; (2) we envisage large language models to become the next-generation computational platform and foster an ecosystem of LLM-based new applications, this naturally requires the foundation models to perform complex tasks that often involve the composition of linguistic and logical operations. Our approach is to compile a suite of challenging reasoning benchmarks to track the progress of LLMs. Our current results show that: (1) model scale clearly correlates with reasoning capabilities; (2) As of May 2023, Claude-v1.3 and PaLM-2 are the only two models that are comparable with GPT-4, while open-sourced models still lag behind; (3) LLaMA-65B performs closely to code-davinci-002, indicating that with successful further development such as reinforcement learning from human feedback (RLHF), it has great potential to be close to GPT-3.5-Turbo. Our results also suggest that for the open-source efforts to catch up, the community may focus more on building better base models and exploring RLHF.

With an increasing social demand for fine-grained sentiment analysis (SA), implicit sentiment analysis (ISA) poses a significant challenge with the absence of salient cue words in expressions. It necessitates reliable reasoning to understand how the sentiment is aroused and thus determine implicit sentiments. In the era of Large Language Models (LLMs), Encoder-Decoder (ED) LLMs have gained popularity to serve as backbone models for SA applications, considering impressive text comprehension and reasoning ability among diverse tasks. On the other hand, Decoder-only (DO) LLMs exhibit superior natural language generation and in-context learning capabilities. However, their responses may contain misleading or inaccurate information. To identify implicit sentiment with reliable reasoning, this study proposes RVISA, a two-stage reasoning framework that harnesses the generation ability of DO LLMs and the reasoning ability of ED LLMs to train an enhanced reasoner. Specifically, we adopt three-hop reasoning prompting to explicitly furnish sentiment elements as cues. The generated rationales are utilized to fine-tune an ED LLM into a skilled reasoner. Additionally, we develop a straightforward yet effective verification mechanism to ensure the reliability of the reasoning learning. We evaluated the proposed method on two benchmark datasets and achieved state-of-the-art results in ISA performance.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose Additional Logic Training (ALT), which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples. We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights. Then, based on these principles, we construct a synthetic corpus named Formal Logic Deduction Diverse (FLD^{times 2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors. Finally, we empirically show that ALT on FLD^{times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B. Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties left{F_{1}, F_{2}, ldots, F_{n}right} and left{W_{1}, W_{2}, ldots, W_{m}right} with associated degrees left{d_{1}, d_{2}, ldots, d_{n}right} and left{e_{1}, e_{2}, ldots, e_{m}right}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W mid F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Reasoning about real-life events is a unifying challenge in AI and NLP that has profound utility in a variety of domains, while fallacy in high-stake applications could be catastrophic. Able to work with diverse text in these domains, large language models (LLMs) have proven capable of answering questions and solving problems. However, I show that end-to-end LLMs still systematically fail to reason about complex events, and they lack interpretability due to their black-box nature. To address these issues, I propose three general approaches to use LLMs in conjunction with a structured representation of events. The first is a language-based representation involving relations of sub-events that can be learned by LLMs via fine-tuning. The second is a semi-symbolic representation involving states of entities that can be predicted and leveraged by LLMs via few-shot prompting. The third is a fully symbolic representation that can be predicted by LLMs trained with structured data and be executed by symbolic solvers. On a suite of event reasoning tasks spanning common-sense inference and planning, I show that each approach greatly outperforms end-to-end LLMs with more interpretability. These results suggest manners of synergy between LLMs and structured representations for event reasoning and beyond.

Reasoning is most powerful when an LLM accurately aggregates relevant information. We examine the critical role of information aggregation in reasoning by requiring the LLM to analyze sports narratives. To succeed at this task, an LLM must infer points from actions, identify related entities, attribute points accurately to players and teams, and compile key statistics to draw conclusions. We conduct comprehensive experiments with real NBA basketball data and present SportsGen, a new method to synthesize game narratives. By synthesizing data, we can rigorously evaluate LLMs' reasoning capabilities under complex scenarios with varying narrative lengths and density of information. Our findings show that most models, including GPT-4o, often fail to accurately aggregate basketball scores due to frequent scoring patterns. Open-source models like Llama-3 further suffer from significant score hallucinations. Finally, the effectiveness of reasoning is influenced by narrative complexity, information density, and domain-specific terms, highlighting the challenges in analytical reasoning tasks.

In this paper, we explore a new way for user targeting, where non-expert marketers could select their target users solely given demands in natural language form. The key to this issue is how to transform natural languages into practical structured logical languages, i.e., the structured understanding of marketer demands. Considering the impressive natural language processing ability of large language models (LLMs), we try to leverage LLMs to solve this issue. Past research indicates that the reasoning ability of LLMs can be effectively enhanced through chain-of-thought (CoT) prompting. But existing methods still have some limitations: (1) Previous methods either use simple "Let's think step by step" spells or provide fixed examples in demonstrations without considering compatibility between prompts and questions, making LLMs ineffective in some complex reasoning tasks such as structured language transformation. (2) Previous methods are often implemented in closed-source models or excessively large models, which is not suitable in industrial practical scenarios. Based on these, we propose ARALLM (i.e., Analogical Reasoning Augmented Large Language Models) consisting of two modules: Analogical Reasoning based Prompting and Reasoning-Augmented Multi-Task Model Distillation.

In this paper, we present an investigative study on how Mental Sets influence the reasoning capabilities of LLMs. LLMs have excelled in diverse natural language processing (NLP) tasks, driven by advancements in parameter-efficient fine-tuning (PEFT) and emergent capabilities like in-context learning (ICL). For complex reasoning tasks, selecting the right model for PEFT or ICL is critical, often relying on scores on benchmarks such as MMLU, MATH, and GSM8K. However, current evaluation methods, based on metrics like F1 Score or reasoning chain assessments by larger models, overlook a key dimension: adaptability to unfamiliar situations and overcoming entrenched thinking patterns. In cognitive psychology, Mental Set refers to the tendency to persist with previously successful strategies, even when they become inefficient - a challenge for problem solving and reasoning. We compare the performance of LLM models like Llama-3.1-8B-Instruct, Llama-3.1-70B-Instruct and GPT-4o in the presence of mental sets. To the best of our knowledge, this is the first study to integrate cognitive psychology concepts into the evaluation of LLMs for complex reasoning tasks, providing deeper insights into their adaptability and problem-solving efficacy.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, the LoT enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%; moreover, it improves Chain-of-Thought with Self-Consistency's performance on LogiQA by +5%; additionally, it boosts performance of Tree-of-Thoughts on ProofWriter dataset by +8%.

In Natural Language Processing (NLP), the Elo rating system, originally designed for ranking players in dynamic games such as chess, is increasingly being used to evaluate Large Language Models (LLMs) through "A vs B" paired comparisons. However, while popular, the system's suitability for assessing entities with constant skill levels, such as LLMs, remains relatively unexplored. We study two fundamental axioms that evaluation methods should adhere to: reliability and transitivity. We conduct extensive evaluation of Elo behaviour, illustrating that individual Elo computations exhibit volatility and delving into the impact of varying the Elo rating system's hyperparameters. We show that these axioms are not always satisfied raising questions about the reliability of current comparative evaluations of LLMs. If the current use of Elo scores is intended to substitute the costly head-to-head comparison of LLMs, it is crucial to ensure the ranking is as robust as possible. Guided by the axioms, our findings offer concrete guidelines for enhancing the reliability of LLM evaluation methods, suggesting a need for reassessment of existing comparative approaches.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

Recent advancement in the capabilities of large language models (LLMs) has triggered a new surge in LLMs' evaluation. Most recent evaluation works tends to evaluate the comprehensive ability of LLMs over series of tasks. However, the deep structure understanding of natural language is rarely explored. In this work, we examine the ability of LLMs to deal with structured semantics on the tasks of question answering with the help of the human-constructed formal language. Specifically, we implement the inter-conversion of natural and formal language through in-context learning of LLMs to verify their ability to understand and generate the structured logical forms. Extensive experiments with models of different sizes and in different formal languages show that today's state-of-the-art LLMs' understanding of the logical forms can approach human level overall, but there still are plenty of room in generating correct logical forms, which suggest that it is more effective to use LLMs to generate more natural language training data to reinforce a small model than directly answering questions with LLMs. Moreover, our results also indicate that models exhibit considerable sensitivity to different formal languages. In general, the formal language with the lower the formalization level, i.e. the more similar it is to natural language, is more LLMs-friendly.

Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However, formal language can cause systematic problems for inductive reasoning such as disability of handling raw input such as natural language, sensitiveness to mislabeled data, and incapacity to handle ambiguous input. To this end, we propose a new paradigm (task) for inductive reasoning, which is to induce natural language rules from natural language facts, and create a dataset termed DEER containing 1.2k rule-fact pairs for the task, where rules and facts are written in natural language. New automatic metrics are also proposed and analysed for the evaluation of this task. With DEER, we investigate a modern approach for inductive reasoning where we use natural language as representation for knowledge instead of formal language and use pretrained language models as ''reasoners''. Moreover, we provide the first and comprehensive analysis of how well pretrained language models can induce natural language rules from natural language facts. We also propose a new framework drawing insights from philosophy literature for this task, which we show in the experiment section that surpasses baselines in both automatic and human evaluations. We discuss about our future perspectives for inductive reasoning in Section 7. Dataset and code are available at https://github.com/ZonglinY/Inductive_Reasoning.

Large language models (LLMs) are primarily evaluated by overall performance on various text understanding and generation tasks. However, such a paradigm fails to comprehensively differentiate the fine-grained language and cognitive skills, rendering the lack of sufficient interpretation to LLMs' capabilities. In this paper, we present FAC^2E, a framework for Fine-grAined and Cognition-grounded LLMs' Capability Evaluation. Specifically, we formulate LLMs' evaluation in a multi-dimensional and explainable manner by dissociating the language-related capabilities and the cognition-related ones. Besides, through extracting the intermediate reasoning from LLMs, we further break down the process of applying a specific capability into three sub-steps: recalling relevant knowledge, utilizing knowledge, and solving problems. Finally, FAC^2E evaluates each sub-step of each fine-grained capability, providing a two-faceted diagnosis for LLMs. Utilizing FAC^2E, we identify a common shortfall in knowledge utilization among models and propose a straightforward, knowledge-enhanced method to mitigate this issue. Our results not only showcase promising performance enhancements but also highlight a direction for future LLM advancements.

Recent availability of Large Language Models (LLMs) has led to the development of numerous LLM-based approaches aimed at providing natural language interfaces for various end-user tasks. These end-user tasks in turn can typically be accomplished by orchestrating a given set of APIs. In practice, natural language task requests (user queries) are often incomplete, i.e., they may not contain all the information required by the APIs. While LLMs excel at natural language processing (NLP) tasks, they frequently hallucinate on missing information or struggle with orchestrating the APIs. The key idea behind our proposed approach is to leverage logical reasoning and classical AI planning along with an LLM for accurately answering user queries including identification and gathering of any missing information in these queries. Our approach uses an LLM and ASP (Answer Set Programming) solver to translate a user query to a representation in Planning Domain Definition Language (PDDL) via an intermediate representation in ASP. We introduce a special API "get_info_api" for gathering missing information. We model all the APIs as PDDL actions in a way that supports dataflow between the APIs. Our approach then uses a classical AI planner to generate an orchestration of API calls (including calls to get_info_api) to answer the user query. Our evaluation results show that our approach significantly outperforms a pure LLM based approach by achieving over 95\% success rate in most cases on a dataset containing complete and incomplete single goal and multi-goal queries where the multi-goal queries may or may not require dataflow among the APIs.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct a systematic study of the inductive reasoning capabilities of LMs through iterative hypothesis refinement, a technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs a three-step process: proposing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal hypothesis proposers (i.e., generating candidate rules), and when coupled with a (task-specific) symbolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling inductive reasoners, showing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.e., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks.

Despite recent advancements in large language models (LLMs), their performance on complex reasoning problems requiring multi-step thinking and combining various skills is still limited. To address this, we propose a novel framework HDFlow for complex reasoning with LLMs that combines fast and slow thinking modes in an adaptive manner. Our approach consists of two key components: 1) a new approach for slow, deliberate reasoning called Dynamic Workflow, which automatically decomposes complex problems into more manageable sub-tasks and dynamically designs a workflow to assemble specialized LLM or symbolic reasoning tools to solve sub-tasks; 2) Hybrid Thinking, a general framework that dynamically combines fast and slow thinking based on problem complexity. Finally, we propose an easy-to-scale method for automatically synthesizing a large-scale dataset of 27K challenging reasoning problems for complex reasoning and a hybrid thinking tuning method that trains smaller LLMs on this dataset to internalize the fast/slow hybrid reasoning strategies. Experiments on four reasoning benchmark datasets demonstrate that our slow thinking with dynamic workflows significantly outperforms Chain-of-Thought, and hybrid thinking achieves the highest accuracy while providing an effective balance between computational efficiency and performance. Fine-tuning using our hybrid thinking approach also significantly boosts the complex reasoning capabilities of open-source language models. The results showcase the promise of slow thinking, dynamic workflows, and hybrid thinking in expanding the frontier of complex problem-solving with LLMsCode and data will be released at \url{https://github.com/wenlinyao/HDFlow.}.

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. While the performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear whether their mathematical reasoning capabilities have genuinely advanced, raising questions about the reliability of the reported metrics. To address these concerns, we conduct a large-scale study on several SOTA open and closed models. To overcome the limitations of existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic templates that allow for the generation of a diverse set of questions. GSM-Symbolic enables more controllable evaluations, providing key insights and more reliable metrics for measuring the reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question. Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models and show that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is because current LLMs cannot perform genuine logical reasoning; they replicate reasoning steps from their training data. Adding a single clause that seems relevant to the question causes significant performance drops (up to 65%) across all state-of-the-art models, even though the clause doesn't contribute to the reasoning chain needed for the final answer. Overall, our work offers a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.

The field of machine learning (ML) has gained widespread adoption, leading to a significant demand for adapting ML to specific scenarios, which is yet expensive and non-trivial. The predominant approaches towards the automation of solving ML tasks (e.g., AutoML) are often time consuming and hard to understand for human developers. In contrast, though human engineers have the incredible ability to understand tasks and reason about solutions, their experience and knowledge are often sparse and difficult to utilize by quantitative approaches. In this paper, we aim to bridge the gap between machine intelligence and human knowledge by introducing a novel framework MLCopilot, which leverages the state-of-the-art LLMs to develop ML solutions for novel tasks. We showcase the possibility of extending the capability of LLMs to comprehend structured inputs and perform thorough reasoning for solving novel ML tasks. And we find that, after some dedicated design, the LLM can (i) observe from the existing experiences of ML tasks and (ii) reason effectively to deliver promising results for new tasks. The solution generated can be used directly to achieve high levels of competitiveness.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

In the field of business data analysis, the ability to extract actionable insights from vast and varied datasets is essential for informed decision-making and maintaining a competitive edge. Traditional rule-based systems, while reliable, often fall short when faced with the complexity and dynamism of modern business data. Conversely, Artificial Intelligence (AI) models, particularly Large Language Models (LLMs), offer significant potential in pattern recognition and predictive analytics but can lack the precision necessary for specific business applications. This paper explores the efficacy of hybrid approaches that integrate the robustness of rule-based systems with the adaptive power of LLMs in generating actionable business insights.

Large language models (LLMs) have shown remarkable performance in reasoning tasks but face limitations in mathematical and complex logical reasoning. Existing methods to improve LLMs' logical capabilities either involve traceable or verifiable logical sequences that generate more reliable responses by constructing logical structures yet increase computational costs, or introduces rigid logic template rules, reducing flexibility. In this paper, we propose Reversal of Thought (RoT), a novel framework aimed at enhancing the logical reasoning abilities of LLMs. RoT utilizes a Preference-Guided Reverse Reasoning warm-up strategy, which integrates logical symbols for pseudocode planning through meta-cognitive mechanisms and pairwise preference self-evaluation to generate task-specific prompts solely through demonstrations, aligning with LLMs' cognitive preferences shaped by Reinforcement Learning with Human Feedback (RLHF). Through reverse reasoning, we ultilize a Cognitive Preference Manager to assess knowledge boundaries and further expand LLMs' reasoning capabilities by aggregating solution logic for known tasks and stylistic templates for unknown tasks. Experiments across various tasks demonstrate that RoT surpasses existing baselines in both reasoning accuracy and efficiency.

Logical reasoning is a critical component of Large Language Models (LLMs), and substantial research efforts in recent years have aimed to enhance their deductive reasoning capabilities. However, existing deductive reasoning benchmarks, which are crucial for evaluating and advancing LLMs, are inadequate due to their lack of task complexity, presence of prior knowledge as a confounder, and superficial error analysis. To address these deficiencies, we introduce JustLogic, a synthetically generated deductive reasoning benchmark designed for rigorous evaluation of LLMs. JustLogic is (i) highly complex, capable of generating a diverse range of linguistic patterns, vocabulary, and argument structures; (ii) prior knowledge independent, eliminating the advantage of models possessing prior knowledge and ensuring that only deductive reasoning is used to answer questions; and (iii) capable of in-depth error analysis on the heterogeneous effects of reasoning depth and argument form on model accuracy. Our experimental results on JustLogic reveal that most state-of-the-art (SOTA) LLMs perform significantly worse than the human average, demonstrating substantial room for model improvement. All code and data are available at https://github.com/michaelchen-lab/JustLogic

Large Language Models (LLMs) have displayed remarkable performances across various complex tasks by leveraging Chain-of-Thought (CoT) prompting. Recently, studies have proposed a Knowledge Distillation (KD) approach, reasoning distillation, which transfers such reasoning ability of LLMs through fine-tuning language models of multi-step rationales generated by LLM teachers. However, they have inadequately considered two challenges regarding insufficient distillation sets from the LLM teacher model, in terms of 1) data quality and 2) soft label provision. In this paper, we propose Mentor-KD, which effectively distills the multi-step reasoning capability of LLMs to smaller LMs while addressing the aforementioned challenges. Specifically, we exploit a mentor, intermediate-sized task-specific fine-tuned model, to augment additional CoT annotations and provide soft labels for the student model during reasoning distillation. We conduct extensive experiments and confirm Mentor-KD's effectiveness across various models and complex reasoning tasks.

Generative artificial intelligence (AI) systems based on large-scale pretrained foundation models (PFMs) such as vision-language models, large language models (LLMs), diffusion models and vision-language-action (VLA) models have demonstrated the ability to solve complex and truly non-trivial AI problems in a wide variety of domains and contexts. Multimodal large language models (MLLMs), in particular, learn from vast and diverse data sources, allowing rich and nuanced representations of the world and, thereby, providing extensive capabilities, including the ability to reason, engage in meaningful dialog; collaborate with humans and other agents to jointly solve complex problems; and understand social and emotional aspects of humans. Despite this impressive feat, the cognitive abilities of state-of-the-art LLMs trained on large-scale datasets are still superficial and brittle. Consequently, generic LLMs are severely limited in their generalist capabilities. A number of foundational problems -- embodiment, symbol grounding, causality and memory -- are required to be addressed for LLMs to attain human-level general intelligence. These concepts are more aligned with human cognition and provide LLMs with inherent human-like cognitive properties that support the realization of physically-plausible, semantically meaningful, flexible and more generalizable knowledge and intelligence. In this work, we discuss the aforementioned foundational issues and survey state-of-the art approaches for implementing these concepts in LLMs. Specifically, we discuss how the principles of embodiment, symbol grounding, causality and memory can be leveraged toward the attainment of artificial general intelligence (AGI) in an organic manner.

In this paper, we present a novel approach, called LogicPro, to enhance Large Language Models (LLMs) complex Logical reasoning through Program Examples. We do this effectively by simply utilizing widely available algorithmic problems and their code solutions. First, we constructed diverse test samples input based on algorithmic questions and code solutions. Then, we designed different complex reasoning questions based on algorithmic problems and test samples. Finally, combining the intermediate variable outputs of the code solutions and the complex reasoning questions, we derived the reasoning process and the final answer. With this approach, we can construct a dataset that is sufficiently difficult (all models are ineffective), diverse (synthesized from 2,360 different algorithmic questions), and scalable (building different test samples and collecting more algorithmic questions). In addition, we obtain a high-quality reasoning process guided by the values of intermediate variables. As a result, our approach achieves significant improvements in multiple models for the BBH^{27}, GSM8K, HellSwag, Logicqa, Reclor, and RTE datasets, outperforming a wide range of existing reasoning datasets.

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

Large language models (LLMs) are restricted to reason in the "language space", where they typically express the reasoning process with a chain-of-thought (CoT) to solve a complex reasoning problem. However, we argue that language space may not always be optimal for reasoning. For example, most word tokens are primarily for textual coherence and not essential for reasoning, while some critical tokens require complex planning and pose huge challenges to LLMs. To explore the potential of LLM reasoning in an unrestricted latent space instead of using natural language, we introduce a new paradigm Coconut (Chain of Continuous Thought). We utilize the last hidden state of the LLM as a representation of the reasoning state (termed "continuous thought"). Rather than decoding this into a word token, we feed it back to the LLM as the subsequent input embedding directly in the continuous space. Experiments show that Coconut can effectively augment the LLM on several reasoning tasks. This novel latent reasoning paradigm leads to emergent advanced reasoning patterns: the continuous thought can encode multiple alternative next reasoning steps, allowing the model to perform a breadth-first search (BFS) to solve the problem, rather than prematurely committing to a single deterministic path like CoT. Coconut outperforms CoT in certain logical reasoning tasks that require substantial backtracking during planning, with fewer thinking tokens during inference. These findings demonstrate the promise of latent reasoning and offer valuable insights for future research.

Chain-of-Thought(CoT) prompting and its variants explore equipping large language models (LLMs) with high-level reasoning abilities by emulating human-like linear cognition and logic. However, the human mind is complicated and mixed with both linear and nonlinear thinking. In this work, we propose Inferential Exclusion Prompting (IEP), a novel prompting that combines the principles of elimination and inference in order to guide LLMs to think non-linearly. IEP guides LLMs to plan and then utilize Natural Language Inference (NLI) to deduce each possible solution's entailment relation with context, commonsense, or facts, therefore yielding a broader perspective by thinking back for inferring. This forward planning and backward eliminating process allows IEP to better simulate the complex human thinking processes compared to other CoT-based methods, which only reflect linear cognitive processes. We conducted a series of empirical studies and have corroborated that IEP consistently outperforms CoT across various tasks. Additionally, we observe that integrating IEP and CoT further improves the LLMs' performance on certain tasks, highlighting the necessity of equipping LLMs with mixed logic processes. Moreover, to better evaluate comprehensive features inherent in human logic, we introduce Mental-Ability Reasoning Benchmark (MARB). The benchmark comprises six novel subtasks with a total of 9,115 questions, among which 1,685 are developed with hand-crafted rationale references. We believe both IEP and MARB can serve as a promising direction for unveiling LLMs' logic and verbal reasoning abilities and drive further advancements. MARB will be available at ~anonymity link soon.

Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Advances in prompt engineering and fine-tuning techniques have further enhanced their ability to address complex reasoning challenges. However, these advanced capabilities are often exclusive to models exceeding 100 billion parameters. Although Chain-of-Thought (CoT) fine-tuning methods have been explored for smaller models (under 10 billion parameters), they typically depend on extensive CoT training data, which can introduce inconsistencies and limit effectiveness in low-data settings. To overcome these limitations, this paper introduce a new reasoning strategy Solution Guidance (SG) and a plug-and-play training paradigm Solution-Guidance Fine-Tuning (SGFT) for enhancing the reasoning capabilities of small language models. SG focuses on problem understanding and decomposition at the semantic and logical levels, rather than specific computations, which can effectively improve the SLMs' generalization and reasoning abilities. With only a small amount of SG training data, SGFT can fine-tune a SLM to produce accurate problem-solving guidances, which can then be flexibly fed to any SLM as prompts, enabling it to generate correct answers directly. Experimental results demonstrate that our method significantly improves the performance of SLMs on various reasoning tasks, enhancing both their practicality and efficiency within resource-constrained environments.

Research is a fundamental process driving the advancement of human civilization, yet it demands substantial time and effort from researchers. In recent years, the rapid development of artificial intelligence (AI) technologies has inspired researchers to explore how AI can accelerate and enhance research. To monitor relevant advancements, this paper presents a systematic review of the progress in this domain. Specifically, we organize the relevant studies into three main categories: hypothesis formulation, hypothesis validation, and manuscript publication. Hypothesis formulation involves knowledge synthesis and hypothesis generation. Hypothesis validation includes the verification of scientific claims, theorem proving, and experiment validation. Manuscript publication encompasses manuscript writing and the peer review process. Furthermore, we identify and discuss the current challenges faced in these areas, as well as potential future directions for research. Finally, we also offer a comprehensive overview of existing benchmarks and tools across various domains that support the integration of AI into the research process. We hope this paper serves as an introduction for beginners and fosters future research. Resources have been made publicly available at https://github.com/zkzhou126/AI-for-Research.

Large language models (LLMs) have accomplished remarkable reasoning performance in various domains. However, in the domain of reasoning tasks, we discover a frailty: LLMs are surprisingly brittle to the ordering of the premises, despite the fact that such ordering does not alter the underlying task. In particular, we observe that LLMs achieve the best performance when the premise order aligns with the context required in intermediate reasoning steps. For example, in deductive reasoning tasks, presenting the premises in the same order as the ground truth proof in the prompt (as opposed to random ordering) drastically increases the model's accuracy. We first examine the effect of premise ordering on deductive reasoning on a variety of LLMs, and our evaluation shows that permuting the premise order can cause a performance drop of over 30%. In addition, we release the benchmark R-GSM, based on GSM8K, to examine the ordering effect for mathematical problem-solving, and we again observe a significant drop in accuracy, relative to the original GSM8K benchmark.

Recent advancements in large language models (LLMs) have propelled Artificial Intelligence (AI) to new heights, enabling breakthroughs in various tasks such as writing assistance, code generation, and machine translation. A significant distinction of advanced LLMs, such as ChatGPT, is their demonstrated ability to "reason." However, evaluating the reasoning ability of LLMs remains a challenge as most existing evaluations focus on their accuracy on the downstream tasks rather than directly assessing their reasoning processes. Efforts have been made to develop benchmarks and metrics to assess reasoning in LLMs, but they suffer from data leakage or limited scope. In this paper, we introduce LogicAsker, an automatic approach that comprehensively evaluates and improves the logical reasoning abilities of LLMs under a set of atomic reasoning skills based on propositional and predicate logic. The results provide insights into LLMs' reasoning abilities and reveal the logical rules the LLMs did not learn well. We evaluate LogicAsker on six widely deployed LLMs, including GPT-3, ChatGPT, GPT-4, Bard, Vicuna, and Guanaco. The results show that test cases from LogicAsker can find logical reasoning failures in different LLMs with a rate of 25\% - 94\%. In addition, the test cases of LogicAsker can be further used to design demonstration examples for in-context learning, which effectively improves the logical reasoning ability of LLMs, e.g., 10\% for GPT-4. As far as we know, our work is the first to create prompts based on testing results to improve LLMs' formal reasoning ability effectively. All the code, data, and results will be released for reproduction and future research.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague semantics based on a lambda calculus where the primitives act on string diagrams rather than logical formulae. As a special case, we show how to translate from the Lambek calculus into Peirce's system beta for first-order logic. This allows us to give a purely diagrammatic treatment of higher-order and non-linear processes in natural language semantics: adverbs, prepositions, negation and quantifiers. The theoretical definition presented in this article comes with a proof-of-concept implementation in DisCoPy, the Python library for string diagrams.

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-boundary.

Existing efforts to improve logical reasoning ability of language models have predominantly relied on supervised fine-tuning, hindering generalization to new domains and/or tasks. The development of Large Langauge Models (LLMs) has demonstrated the capacity of compressing abundant knowledge into a single proxy, enabling them to tackle multiple tasks effectively. Our preliminary experiments, nevertheless, show that LLMs do not show capability on logical reasoning. The performance of LLMs on logical reasoning benchmarks is far behind the existing state-of-the-art baselines. In this paper, we make the first attempt to investigate the feasibility of incorporating logical knowledge through self-supervised post-training, and activating it via in-context learning, which we termed as LogicLLM. Specifically, we devise an auto-regressive objective variant of MERIt and integrate it with two LLM series, i.e., FLAN-T5 and LLaMA, with parameter size ranging from 3 billion to 13 billion. The results on two challenging logical reasoning benchmarks demonstrate the effectiveness of LogicLLM. Besides, we conduct extensive ablation studies to analyze the key factors in designing logic-oriented proxy tasks.

Large Language Models (LLMs) are deployed as powerful tools for several natural language processing (NLP) applications. Recent works show that modern LLMs can generate self-explanations (SEs), which elicit their intermediate reasoning steps for explaining their behavior. Self-explanations have seen widespread adoption owing to their conversational and plausible nature. However, there is little to no understanding of their faithfulness. In this work, we discuss the dichotomy between faithfulness and plausibility in SEs generated by LLMs. We argue that while LLMs are adept at generating plausible explanations -- seemingly logical and coherent to human users -- these explanations do not necessarily align with the reasoning processes of the LLMs, raising concerns about their faithfulness. We highlight that the current trend towards increasing the plausibility of explanations, primarily driven by the demand for user-friendly interfaces, may come at the cost of diminishing their faithfulness. We assert that the faithfulness of explanations is critical in LLMs employed for high-stakes decision-making. Moreover, we urge the community to identify the faithfulness requirements of real-world applications and ensure explanations meet those needs. Finally, we propose some directions for future work, emphasizing the need for novel methodologies and frameworks that can enhance the faithfulness of self-explanations without compromising their plausibility, essential for the transparent deployment of LLMs in diverse high-stakes domains.

Large language models (LLMs) have demonstrated outstanding performance across various tasks, yet they still exhibit limitations such as hallucination, unfaithful reasoning, and toxic content. One potential approach to mitigate these issues is learning from human or external feedback (e.g. tools). In this paper, we introduce an intrinsic self-correct reasoning framework for LLMs that eliminates the need for human feedback, external tools, and handcraft prompts. The proposed framework, based on a multi-step reasoning paradigm Learning from Correctness (LeCo), improves reasoning performance without needing to learn from errors. This paradigm prioritizes learning from correct reasoning steps, and a unique method to measure confidence for each reasoning step based on generation logits. Experimental results across various multi-step reasoning tasks demonstrate the effectiveness of the framework in improving reasoning performance with reduced token consumption.

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

Large language models (LLMs) have shown remarkable reasoning capabilities, especially when prompted to generate intermediate reasoning steps (e.g., Chain-of-Thought, CoT). However, LLMs can still struggle with problems that are easy for humans, such as generating action plans for executing tasks in a given environment, or performing complex math, logical, and commonsense reasoning. The deficiency stems from the key fact that LLMs lack an internal world model to predict the world state (e.g., environment status, intermediate variable values) and simulate long-term outcomes of actions. This prevents LLMs from performing deliberate planning akin to human brains, which involves exploring alternative reasoning paths, anticipating future states and rewards, and iteratively refining existing reasoning steps. To overcome the limitations, we propose a new LLM reasoning framework, Reasoning via Planning (RAP). RAP repurposes the LLM as both a world model and a reasoning agent, and incorporates a principled planning algorithm (based on Monto Carlo Tree Search) for strategic exploration in the vast reasoning space. During reasoning, the LLM (as agent) incrementally builds a reasoning tree under the guidance of the LLM (as world model) and task-specific rewards, and obtains a high-reward reasoning path efficiently with a proper balance between exploration vs. exploitation. We apply RAP to a variety of challenging reasoning problems including plan generation, math reasoning, and logical inference. Empirical results on these tasks demonstrate the superiority of RAP over various strong baselines, including CoT and least-to-most prompting with self-consistency. RAP on LLAMA-33B surpasses CoT on GPT-4 with 33% relative improvement in a plan generation setting.

Building systems that are good for society in the face of complex societal effects requires a dynamic approach. Recent approaches to machine learning (ML) documentation have demonstrated the promise of discursive frameworks for deliberation about these complexities. However, these developments have been grounded in a static ML paradigm, leaving the role of feedback and post-deployment performance unexamined. Meanwhile, recent work in reinforcement learning has shown that the effects of feedback and optimization objectives on system behavior can be wide-ranging and unpredictable. In this paper we sketch a framework for documenting deployed and iteratively updated learning systems, which we call Reward Reports. Taking inspiration from various contributions to the technical literature on reinforcement learning, we outline Reward Reports as living documents that track updates to design choices and assumptions behind what a particular automated system is optimizing for. They are intended to track dynamic phenomena arising from system deployment, rather than merely static properties of models or data. After presenting the elements of a Reward Report, we discuss a concrete example: Meta's BlenderBot 3 chatbot. Several others for game-playing (DeepMind's MuZero), content recommendation (MovieLens), and traffic control (Project Flow) are included in the appendix.

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.

To enable Large Language Models (LLMs) to function as conscious agents with generalizable reasoning capabilities, it is crucial that they possess the reasoning ability to comprehend situational changes (transitions) in distribution triggered by environmental factors or actions from other agents. Despite its fundamental significance, this ability remains underexplored due to the complexity of modeling infinite possible changes in an event and their associated distributions, coupled with the lack of benchmark data with situational transitions. Addressing these gaps, we propose a novel formulation of reasoning with distributional changes as a three-step discriminative process, termed as MetAphysical ReaSoning. We then introduce the first-ever benchmark, MARS, comprising three tasks corresponding to each step. These tasks systematically assess LLMs' capabilities in reasoning the plausibility of (i) changes in actions, (ii) states caused by changed actions, and (iii) situational transitions driven by changes in action. Extensive evaluations with 20 (L)LMs of varying sizes and methods indicate that all three tasks in this process pose significant challenges, even for state-of-the-art LLMs and LMs after fine-tuning. Further analyses reveal potential causes for the underperformance of LLMs and demonstrate that pre-training them on large-scale conceptualization taxonomies can potentially enhance their metaphysical reasoning capabilities. Our data and models are publicly accessible at https://github.com/HKUST-KnowComp/MARS.

Translating natural language sentences to first-order logic (NL-FOL translation) is a longstanding challenge in the NLP and formal logic literature. This paper introduces LogicLLaMA, a LLaMA-7B model fine-tuned for NL-FOL translation using LoRA on a single GPU. LogicLLaMA is capable of directly translating natural language into FOL rules, which outperforms GPT-3.5. LogicLLaMA is also equipped to correct FOL rules predicted by GPT-3.5, and can achieve similar performance as GPT-4 with a fraction of the cost. This correction ability was achieved by a novel supervised fine-tuning (SFT) + reinforcement learning with human feedback (RLHF) framework, which initially trains on synthetically perturbed NL-FOL pairs to encourage chain-of-thought reasoning and then fine-tunes with RLHF on GPT-3.5 outputs using a FOL verifier as the reward model. To train LogicLLaMA, we present MALLS (large language Model generAted NL-FOL pairS), a dataset of 34K high-quality and diverse sentence-level NL-FOL pairs collected from GPT-4. The dataset was created by implementing a pipeline that prompts GPT-4 for pairs, and dynamically adjusts the prompts to ensure the collection of pairs with rich and diverse contexts at different levels of complexity, and verifies the validity of the generated FOL rules. Codes, weights, and data are available at https://github.com/gblackout/LogicLLaMA{{small https://github.com/gblackout/LogicLLaMA}}.

Large Language Models (LLMs) have shown remarkable capabilities in code generation tasks, yet they face significant limitations in handling complex, long-context programming challenges and demonstrating complex compositional reasoning abilities. This paper introduces a novel agentic framework for ``guided code generation'' that tries to address these limitations through a deliberately structured, fine-grained approach to code generation tasks. Our framework leverages LLMs' strengths as fuzzy searchers and approximate information retrievers while mitigating their weaknesses in long sequential reasoning and long-context understanding. Empirical evaluation using OpenAI's HumanEval benchmark with Meta's Llama 3.1 8B model (int4 precision) demonstrates a 23.79\% improvement in solution accuracy compared to direct one-shot generation. Our results indicate that structured, guided approaches to code generation can significantly enhance the practical utility of LLMs in software development while overcoming their inherent limitations in compositional reasoning and context handling.

In this paper, we explain the inference logic of large language models (LLMs) as a set of symbolic concepts. Many recent studies have discovered that traditional DNNs usually encode sparse symbolic concepts. However, because an LLM has much more parameters than traditional DNNs, whether the LLM also encodes sparse symbolic concepts is still an open problem. Therefore, in this paper, we propose to disentangle the inference score of LLMs for dialogue tasks into a small number of symbolic concepts. We verify that we can use those sparse concepts to well estimate all inference scores of the LLM on all arbitrarily masking states of the input sentence. We also evaluate the transferability of concepts encoded by an LLM and verify that symbolic concepts usually exhibit high transferability across similar input sentences. More crucially, those symbolic concepts can be used to explain the exact reasons accountable for the LLM's prediction errors.

Large Language Models (LLMs) have demonstrated good performance in many reasoning tasks, but they still struggle with some complicated reasoning tasks including logical reasoning. One non-negligible reason for LLMs' suboptimal performance on logical reasoning is their overlooking of understanding logical fallacies correctly. To evaluate LLMs' capability of logical fallacy understanding (LFU), we propose five concrete tasks from three cognitive dimensions of WHAT, WHY, and HOW in this paper. Towards these LFU tasks, we have successfully constructed a new dataset LFUD based on GPT-4 accompanied by a little human effort. Our extensive experiments justify that our LFUD can be used not only to evaluate LLMs' LFU capability, but also to fine-tune LLMs to obtain significantly enhanced performance on logical reasoning.

Chain-of-Thought (CoT) Prompting is a dominant paradigm in Large Language Models (LLMs) to enhance complex reasoning. It guides LLMs to present multi-step reasoning, rather than generating the final answer directly. However, CoT encounters difficulties when key information required for reasoning is implicit or missing. This occurs because CoT emphasizes the sequence of reasoning steps while overlooking the early extraction of essential information. We propose a pre-prompting method called Iterative Summarization Pre-Prompting (ISP^2) to refine LLM reasoning when key information is not explicitly provided. First, entities and their corresponding descriptions are extracted to form potential key information pairs. Next, we use a reliability rating to assess these pairs, then merge the two lowest-ranked pairs into a new entity description. This process is repeated until a unique key information pair is obtained. Finally, that pair, along with the original question, is fed into LLMs to produce the answer. Extensive experiments demonstrate a 7.1% improvement compared to existing methods. Unlike traditional prompting, ISP^2 adopts an inductive approach with pre-prompting, offering flexible integration into diverse reasoning frameworks. The code is available at https://github.com/zdhgreat/ISP-2.

Large language models (LLMs) have demonstrated human-level performance on a vast spectrum of natural language tasks. However, few studies have addressed the LLM threat and vulnerability from an ideology perspective, especially when they are increasingly being deployed in sensitive domains, e.g., elections and education. In this study, we explore the implications of GPT soft ideologization through the use of AI-self-consciousness. By utilizing GPT self-conversations, AI can be granted a vision to "comprehend" the intended ideology, and subsequently generate finetuning data for LLM ideology injection. When compared to traditional government ideology manipulation techniques, such as information censorship, LLM ideologization proves advantageous; it is easy to implement, cost-effective, and powerful, thus brimming with risks.

Chain-of-Thought (CoT) reasoning has enabled Large Language Model (LLM) to achieve remarkable performance in various NLP tasks, including arithmetic problem-solving. However, this success does not generalize to small language model (sLM) like T5, due to their limited capacity and absence of emergent abilities associated with larger models. Recent works to enhance sLM through knowledge distillation have yielded some improvements but still face significant limitations, particularly high ambiguity from the variability in natural language expressions and substantial computational costs. In this paper, we investigate why sLM perform poorly on arithmetic reasoning tasks and hypothesize that natural language format variability introduces high ambiguity for these smaller models. Based on this hypothesis, we conduct experiments with equation-only format, which is a reasoning format that unifies arithmetic reasoning previously expressed in natural language formats into mathematical equations. Experiment results demonstrate that equation-only format effectively boosts the arithmetic reasoning abilities of sLM, especially in very small models like T5-Tiny.

Large Language Models (LLMs) have demonstrated significant potential in handling complex reasoning tasks through step-by-step rationale generation. However, recent studies have raised concerns regarding the hallucination and flaws in their reasoning process. Substantial efforts are being made to improve the reliability and faithfulness of the generated rationales. Some approaches model reasoning as planning, while others focus on annotating for process supervision. Nevertheless, the planning-based search process often results in high latency due to the frequent assessment of intermediate reasoning states and the extensive exploration space. Additionally, supervising the reasoning process with human annotation is costly and challenging to scale for LLM training. To address these issues, in this paper, we propose a framework to learn planning-based reasoning through direct preference optimization (DPO) on collected trajectories, which are ranked according to synthesized process rewards. Our results on challenging logical reasoning benchmarks demonstrate the effectiveness of our learning framework, showing that our 7B model can surpass the strong counterparts like GPT-3.5-Turbo.

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, their reasoning can be unsound, inconsistent, or rely on undesirable prior assumptions. To tackle these issues, we introduce a class of tools for language models called guides that use state and incremental constraints to guide generation. A guide can be invoked by the model to constrain its own generation to a set of valid statements given by the tool. In turn, the model's choices can change the guide's state. We show how a general system for logical reasoning can be used as a guide, which we call LogicGuide. Given a reasoning problem in natural language, a model can formalize its assumptions for LogicGuide and then guarantee that its reasoning steps are sound. In experiments with the PrOntoQA and ProofWriter reasoning datasets, LogicGuide significantly improves the performance of GPT-3, GPT-3.5 Turbo and LLaMA (accuracy gains up to 35%). LogicGuide also drastically reduces content effects: the interference of prior and current assumptions that both humans and language models have been shown to suffer from. Finally, we explore bootstrapping LLaMA 13B from its own reasoning and find that LogicGuide is critical: by training only on certified self-generated reasoning, LLaMA can self-improve, avoiding learning from its own hallucinations.

In recent months, Language Models (LMs) have become a part of daily discourse, with focus on OpenAI and the potential of Artificial General Intelligence (AGI). Furthermore, the leaking of LLama's weights to the public has led to an influx of innovations demonstrating the impressive capabilities of generative LMs. While we believe that AGI is still a distant goal, we recognize the potential of LMs in solving tasks such as searching complex documents, compiling reports with basic analysis, and providing assistance in problem-solving. In this paper, we propose formalizing the execution model of language models. We investigate current execution models, to find that this formalism has received little attention, and present our contribution: the first formalized execution model for LMs. We introduce a new algorithm for sampling the predictions of LMs, which we use to build a reliable and inspectable execution model. We introduce a low-level language to write "cognitive program" for this execution model. We hope to shed light on the need for execution models for LMs and encourage further research in this area.

Background: Large language models (LLMs) are trained to follow directions, but this introduces a vulnerability to blindly comply with user requests even if they generate wrong information. In medicine, this could accelerate the generation of misinformation that impacts human well-being. Objectives/Methods: We analyzed compliance to requests to generate misleading content about medications in settings where models know the request is illogical. We investigated whether in-context directions and instruction-tuning of LLMs to prioritize logical reasoning over compliance reduced misinformation risk. Results: While all frontier LLMs complied with misinformation requests, both prompt-based and parameter-based approaches can improve the detection of logic flaws in requests and prevent the dissemination of medical misinformation. Conclusion: Shifting LLMs to prioritize logic over compliance could reduce risks of exploitation for medical misinformation.

Remarkable performance of large language models (LLMs) in a variety of tasks brings forth many opportunities as well as challenges of utilizing them in production settings. Towards practical adoption of LLMs, multi-agent systems hold great promise to augment, integrate, and orchestrate LLMs in the larger context of enterprise platforms that use existing proprietary data and models to tackle complex real-world tasks. Despite the tremendous success of these systems, current approaches rely on narrow, single-focus objectives for optimization and evaluation, often overlooking potential constraints in real-world scenarios, including restricted budgets, resources and time. Furthermore, interpreting, analyzing, and debugging these systems requires different components to be evaluated in relation to one another. This demand is currently not feasible with existing methodologies. In this postion paper, we introduce the concept of reasoning capacity as a unifying criterion to enable integration of constraints during optimization and establish connections among different components within the system, which also enable a more holistic and comprehensive approach to evaluation. We present a formal definition of reasoning capacity and illustrate its utility in identifying limitations within each component of the system. We then argue how these limitations can be addressed with a self-reflective process wherein human-feedback is used to alleviate shortcomings in reasoning and enhance overall consistency of the system.

Large Language Models (LLMs) have demonstrated impressive capability in many nature language tasks. However, the auto-regressive generation process makes LLMs prone to produce errors, hallucinations and inconsistent statements when performing multi-step reasoning. In this paper, we aim to alleviate the pathology by introducing Q*, a general, versatile and agile framework for guiding LLMs decoding process with deliberative planning. By learning a plug-and-play Q-value model as heuristic function, our Q* can effectively guide LLMs to select the most promising next step without fine-tuning LLMs for each task, which avoids the significant computational overhead and potential risk of performance degeneration on other tasks. Extensive experiments on GSM8K, MATH and MBPP confirm the superiority of our method.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

Parallel neurosymbolic architectures have been applied effectively in NLP by distilling knowledge from a logic theory into a deep model.However, prior art faces several limitations including supporting restricted forms of logic theories and relying on the assumption of independence between the logic and the deep network. We present Concordia, a framework overcoming the limitations of prior art. Concordia is agnostic both to the deep network and the logic theory offering support for a wide range of probabilistic theories. Our framework can support supervised training of both components and unsupervised training of the neural component. Concordia has been successfully applied to tasks beyond NLP and data classification, improving the accuracy of state-of-the-art on collective activity detection, entity linking and recommendation tasks.

The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical knowledge. However, we demonstrate that, when methodically questioned, large language models (LLMs) often display and demonstrate significant inconsistencies in their knowledge. Computationally, the basic aspects of the conceptualization of a given domain can be represented as Is-A hierarchies in a knowledge graph (KG) or ontology, together with a few properties or axioms that enable straightforward reasoning. We show that even simple ontologies can be used to reveal conceptual inconsistencies across several LLMs. We also propose strategies that domain experts can use to evaluate and improve the coverage of key domain concepts in LLMs of various sizes. In particular, we have been able to significantly enhance the performance of LLMs of various sizes with openly available weights using simple knowledge-graph (KG) based prompting strategies.

One of the fundamental challenges in reinforcement learning (RL) is to take a complex task and be able to decompose it to subtasks that are simpler for the RL agent to learn. In this paper, we report on our work that would identify subtasks by using some given positive and negative trajectories for solving the complex task. We assume that the states are represented by first-order predicate logic using which we devise a novel algorithm to identify the subtasks. Then we employ a Large Language Model (LLM) to generate first-order logic rule templates for achieving each subtask. Such rules were then further fined tuned to a rule-based policy via an Inductive Logic Programming (ILP)-based RL agent. Through experiments, we verify the accuracy of our algorithm in detecting subtasks which successfully detect all of the subtasks correctly. We also investigated the quality of the common-sense rules produced by the language model to achieve the subtasks. Our experiments show that our LLM-guided rule template generation can produce rules that are necessary for solving a subtask, which leads to solving complex tasks with fewer assumptions about predefined first-order logic predicates of the environment.

The advancement of machine learning and symbolic approaches have underscored their strengths and weaknesses in Natural Language Processing (NLP). While machine learning approaches are powerful in identifying patterns in data, they often fall short in learning commonsense and the factual knowledge required for the NLP tasks. Meanwhile, the symbolic methods excel in representing knowledge-rich data. However, they struggle to adapt dynamic data and generalize the knowledge. Bridging these two paradigms through hybrid approaches enables the alleviation of weaknesses in both while preserving their strengths. Recent studies extol the virtues of this union, showcasing promising results in a wide range of NLP tasks. In this paper, we present an overview of hybrid approaches used for NLP. Specifically, we delve into the state-of-the-art hybrid approaches used for a broad spectrum of NLP tasks requiring natural language understanding, generation, and reasoning. Furthermore, we discuss the existing resources available for hybrid approaches for NLP along with the challenges, offering a roadmap for future directions.

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe

If machine learning models were to achieve superhuman abilities at various reasoning or decision-making tasks, how would we go about evaluating such models, given that humans would necessarily be poor proxies for ground truth? In this paper, we propose a framework for evaluating superhuman models via consistency checks. Our premise is that while the correctness of superhuman decisions may be impossible to evaluate, we can still surface mistakes if the model's decisions fail to satisfy certain logical, human-interpretable rules. We instantiate our framework on three tasks where correctness of decisions is hard to evaluate due to either superhuman model abilities, or to otherwise missing ground truth: evaluating chess positions, forecasting future events, and making legal judgments. We show that regardless of a model's (possibly superhuman) performance on these tasks, we can discover logical inconsistencies in decision making. For example: a chess engine assigning opposing valuations to semantically identical boards; GPT-4 forecasting that sports records will evolve non-monotonically over time; or an AI judge assigning bail to a defendant only after we add a felony to their criminal record.

LLM-based agents have recently emerged as promising tools for solving challenging problems without the need for task-specific finetuned models that can be expensive to procure. Currently, the design and implementation of such agents is ad hoc, as the wide variety of tasks that LLM-based agents may be applied to naturally means there can be no one-size-fits-all approach to agent design. In this work we aim to alleviate the difficulty of designing and implementing new agents by proposing a minimalistic, high-level generation framework that simplifies the process of building agents. The framework we introduce allows the user to specify desired agent behaviors in Linear Temporal Logic (LTL). The declarative LTL specification is then used to construct a constrained decoder that guarantees the LLM will produce an output exhibiting the desired behavior. By designing our framework in this way, we obtain several benefits, including the ability to enforce complex agent behavior, the ability to formally validate prompt examples, and the ability to seamlessly incorporate content-focused logical constraints into generation. In particular, our declarative approach, in which the desired behavior is simply described without concern for how it should be implemented or enforced, enables rapid design, implementation and experimentation with different LLM-based agents. We demonstrate how the proposed framework can be used to implement recent LLM-based agents, and show how the guardrails our approach provides can lead to improvements in agent performance. In addition, we release our code for general use.

Implicit Personalization (IP) is a phenomenon of language models inferring a user's background from the implicit cues in the input prompts and tailoring the response based on this inference. While previous work has touched upon various instances of this problem, there lacks a unified framework to study this behavior. This work systematically studies IP through a rigorous mathematical formulation, a multi-perspective moral reasoning framework, and a set of case studies. Our theoretical foundation for IP relies on a structural causal model and introduces a novel method, indirect intervention, to estimate the causal effect of a mediator variable that cannot be directly intervened upon. Beyond the technical approach, we also introduce a set of moral reasoning principles based on three schools of moral philosophy to study when IP may or may not be ethically appropriate. Equipped with both mathematical and ethical insights, we present three diverse case studies illustrating the varied nature of the IP problem and offer recommendations for future research. Our code and data are at https://github.com/jiarui-liu/IP.

The integration of slow-thinking mechanisms into large language models (LLMs) offers a promising way toward achieving Level 2 AGI Reasoners, as exemplified by systems like OpenAI's o1. However, several significant challenges remain, including inefficient overthinking and an overreliance on auxiliary reward models. We point out that these limitations stem from LLMs' inability to internalize the search process, a key component of effective reasoning. A critical step toward addressing this issue is enabling LLMs to autonomously determine when and where to backtrack, a fundamental operation in traditional search algorithms. To this end, we propose a self-backtracking mechanism that equips LLMs with the ability to backtrack during both training and inference. This mechanism not only enhances reasoning ability but also efficiency by transforming slow-thinking processes into fast-thinking through self-improvement. Empirical evaluations demonstrate that our proposal significantly enhances the reasoning capabilities of LLMs, achieving a performance gain of over 40 percent compared to the optimal-path supervised fine-tuning method. We believe this study introduces a novel and promising pathway for developing more advanced and robust Reasoners.

Large language models (LLMs) have demonstrated remarkable performance in a range of natural language understanding and generation tasks. Yet, their ability to generate counterfactuals, which can be used for areas like data augmentation, remains under-explored. This study aims to investigate the counterfactual generation capabilities of LLMs and analysis factors that influence this ability. First, we evaluate how effective are LLMs in counterfactual generation through data augmentation experiments for small language models (SLMs) across four tasks: sentiment analysis, natural language inference, named entity recognition, and relation extraction. While LLMs show promising enhancements in various settings, they struggle in complex tasks due to their self-limitations and the lack of logical guidance to produce counterfactuals that align with commonsense. Second, our analysis reveals the pivotal role of providing accurate task definitions and detailed step-by-step instructions to LLMs in generating counterfactuals. Interestingly, we also find that LLMs can generate reasonable counterfactuals even with unreasonable demonstrations, which illustrates that demonstrations are primarily to regulate the output format.This study provides the first comprehensive insight into counterfactual generation abilities of LLMs, and offers a novel perspective on utilizing LLMs for data augmentation to enhance SLMs.

Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) have made significant advancements in reasoning capabilities. However, they still face challenges such as high computational demands and privacy concerns. This paper focuses on developing efficient Small Language Models (SLMs) and Multimodal Small Language Models (MSLMs) that retain competitive reasoning abilities. We introduce a novel training pipeline that enhances reasoning capabilities and facilitates deployment on edge devices, achieving state-of-the-art performance while minimizing development costs. \InfR~ aims to advance AI systems by improving reasoning, reducing adoption barriers, and addressing privacy concerns through smaller model sizes. Resources are available at https://github. com/Reallm-Labs/InfiR.

The notion of variation is introduced for the Boolean set and based on which Boolean logic backpropagation principle is developed. Using this concept, deep models can be built with weights and activations being Boolean numbers and operated with Boolean logic instead of real arithmetic. In particular, Boolean deep models can be trained directly in the Boolean domain without latent weights. No gradient but logic is synthesized and backpropagated through layers.

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.

We explore whether Large Language Models (LLMs) are capable of logical reasoning with distorted facts, which we call Deduction under Perturbed Evidence (DUPE). DUPE presents a unique challenge to LLMs since they typically rely on their parameters, which encode mostly accurate information, to reason and make inferences. However, in DUPE, LLMs must reason over manipulated or falsified evidence present in their prompts, which can result in false conclusions that are valid only under the manipulated evidence. Our goal with DUPE is to determine whether LLMs can arrive at these false conclusions and identify whether the dominant factor influencing the deduction process is the encoded data in the parameters or the manipulated evidence in the prompts. To evaluate the DUPE capabilities of LLMs, we create a DUPEd version of the StrategyQA dataset, where facts are manipulated to reverse the answer to the question. Our findings show that even the most advanced GPT models struggle to reason on manipulated facts - showcasing poor DUPE skills - with accuracy dropping by 45% compared to the original dataset. We also investigate prompt settings inspired from student simulation models, which mitigate the accuracy drop to some extent. Our findings have practical implications for understanding the performance of LLMs in real-world applications such as student simulation models that involve reasoning over inaccurate information.

Large language models (LLMs) are becoming increasingly important for machine learning applications. However, it can be challenging to align LLMs with our intent, particularly when we want to generate content that is preferable over others or when we want the LLM to respond in a certain style or tone that is hard to describe. To address this challenge, we propose an approach that uses contrastive examples to better describe our intent. This involves providing positive examples that illustrate the true intent, along with negative examples that show what characteristics we want LLMs to avoid. The negative examples can be retrieved from labeled data, written by a human, or generated by the LLM itself. Before generating an answer, we ask the model to analyze the examples to teach itself what to avoid. This reasoning step provides the model with the appropriate articulation of the user's need and guides it towards generting a better answer. We tested our approach on both synthesized and real-world datasets, including StackExchange and Reddit, and found that it significantly improves performance compared to standard few-shot prompting

Huge language models (LMs) have ushered in a new era for AI, serving as a gateway to natural-language-based knowledge tasks. Although an essential element of modern AI, LMs are also inherently limited in a number of ways. We discuss these limitations and how they can be avoided by adopting a systems approach. Conceptualizing the challenge as one that involves knowledge and reasoning in addition to linguistic processing, we define a flexible architecture with multiple neural models, complemented by discrete knowledge and reasoning modules. We describe this neuro-symbolic architecture, dubbed the Modular Reasoning, Knowledge and Language (MRKL, pronounced "miracle") system, some of the technical challenges in implementing it, and Jurassic-X, AI21 Labs' MRKL system implementation.

Large Language Models (LLMs) have performed well on various reasoning tasks, but their inaccessibility and numerous parameters hinder wide application in practice. One promising way is distilling the reasoning ability from LLMs to small models by the generated chain-of-thought reasoning paths. In some cases, however, LLMs may produce incorrect reasoning chains, especially when facing complex mathematical problems. Previous studies only transfer knowledge from positive samples and drop the synthesized data with wrong answers. In this work, we illustrate the merit of negative data and propose a model specialization framework to distill LLMs with negative samples besides positive ones. The framework consists of three progressive steps, covering from training to inference stages, to absorb knowledge from negative data. We conduct extensive experiments across arithmetic reasoning tasks to demonstrate the role of negative data in distillation from LLM.

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/ .

Large Language Models (LLMs) have shown to be capable of various tasks, yet their capability in interpreting and reasoning over tabular data remains an underexplored area. In this context, this study investigates from three core perspectives: the robustness of LLMs to structural perturbations in tables, the comparative analysis of textual and symbolic reasoning on tables, and the potential of boosting model performance through the aggregation of multiple reasoning pathways. We discover that structural variance of tables presenting the same content reveals a notable performance decline, particularly in symbolic reasoning tasks. This prompts the proposal of a method for table structure normalization. Moreover, textual reasoning slightly edges out symbolic reasoning, and a detailed error analysis reveals that each exhibits different strengths depending on the specific tasks. Notably, the aggregation of textual and symbolic reasoning pathways, bolstered by a mix self-consistency mechanism, resulted in achieving SOTA performance, with an accuracy of 73.6% on WIKITABLEQUESTIONS, representing a substantial advancement over previous existing table processing paradigms of LLMs.

In this paper, we present a novel framework for the analysis of Riemann Hypothesis [27], which is composed of three key components: a) probabilistic modeling with cross entropy optimization and reasoning; b) the application of the law of large numbers; c) the application of mathematical inductions. The analysis is mainly conducted by virtue of probabilistic modeling of cross entropy optimization and reasoning with rare event simulation techniques. The application of the law of large numbers [2, 3, 6] and the application of mathematical inductions make the analysis of Riemann Hypothesis self-contained and complete to make sure that the whole complex plane is covered as conjectured in Riemann Hypothesis. We also discuss the method of enhanced top-p sampling with large language models (LLMs) for reasoning, where next token prediction is not just based on the estimated probabilities of each possible token in the current round but also based on accumulated path probabilities among multiple top-k chain of thoughts (CoTs) paths. The probabilistic modeling of cross entropy optimization and reasoning may suit well with the analysis of Riemann Hypothesis as Riemann Zeta functions are inherently dealing with the sums of infinite components of a complex number series. We hope that our analysis in this paper could shed some light on some of the insights of Riemann Hypothesis. The framework and techniques presented in this paper, coupled with recent developments with chain of thought (CoT) or diagram of thought (DoT) reasoning in large language models (LLMs) with reinforcement learning (RL) [1, 7, 18, 21, 24, 34, 39-41], could pave the way for eventual proof of Riemann Hypothesis [27].

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Multi-modal Large Language Models (MLLMs) are increasingly prominent in the field of artificial intelligence. These models not only excel in traditional vision-language tasks but also demonstrate impressive performance in contemporary multi-modal benchmarks. Although many of these benchmarks attempt to holistically evaluate MLLMs, they typically concentrate on basic reasoning tasks, often yielding only simple yes/no or multi-choice responses. These methods naturally lead to confusion and difficulties in conclusively determining the reasoning capabilities of MLLMs. To mitigate this issue, we manually curate a benchmark dataset specifically designed for MLLMs, with a focus on complex reasoning tasks. Our benchmark comprises three key reasoning categories: deductive, abductive, and analogical reasoning. The queries in our dataset are intentionally constructed to engage the reasoning capabilities of MLLMs in the process of generating answers. For a fair comparison across various MLLMs, we incorporate intermediate reasoning steps into our evaluation criteria. In instances where an MLLM is unable to produce a definitive answer, its reasoning ability is evaluated by requesting intermediate reasoning steps. If these steps align with our manual annotations, appropriate scores are assigned. This evaluation scheme resembles methods commonly used in human assessments, such as exams or assignments, and represents what we consider a more effective assessment technique compared with existing benchmarks. We evaluate a selection of representative MLLMs using this rigorously developed open-ended multi-step elaborate reasoning benchmark, designed to challenge and accurately measure their reasoning capabilities. The code and data will be released at https://core-mm.github.io/

In this paper, we present a new theoretical approach for enabling domain knowledge acquisition by intelligent systems. We introduce a hybrid model that starts with minimal input knowledge in the form of an upper ontology of concepts, stores and reasons over this knowledge through a knowledge graph database and learns new information through a Logic Neural Network. We study the behavior of this architecture when handling new data and show that the final system is capable of enriching its current knowledge as well as extending it to new domains.

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.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

We present Step-Back Prompting, a simple prompting technique that enables LLMs to do abstractions to derive high-level concepts and first principles from instances containing specific details. Using the concepts and principles to guide the reasoning steps, LLMs significantly improve their abilities in following a correct reasoning path towards the solution. We conduct experiments of Step-Back Prompting with PaLM-2L models and observe substantial performance gains on a wide range of challenging reasoning-intensive tasks including STEM, Knowledge QA, and Multi-Hop Reasoning. For instance, Step-Back Prompting improves PaLM-2L performance on MMLU Physics and Chemistry by 7% and 11%, TimeQA by 27%, and MuSiQue by 7%.

In the last years many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The literature reports many approaches aimed at overcoming this crucial weakness sometimes at the cost of scarifying accuracy for interpretability. The applications in which black box decision systems can be used are various, and each approach is typically developed to provide a solution for a specific problem and, as a consequence, delineating explicitly or implicitly its own definition of interpretability and explanation. The aim of this paper is to provide a classification of the main problems addressed in the literature with respect to the notion of explanation and the type of black box system. Given a problem definition, a black box type, and a desired explanation this survey should help the researcher to find the proposals more useful for his own work. The proposed classification of approaches to open black box models should also be useful for putting the many research open questions in perspective.

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

Analytical reasoning is an essential and challenging task that requires a system to analyze a scenario involving a set of particular circumstances and perform reasoning over it to make conclusions. In this paper, we study the challenge of analytical reasoning of text and introduce a new dataset consisting of questions from the Law School Admission Test from 1991 to 2016. We analyze what knowledge understanding and reasoning abilities are required to do well on this task. Furthermore, to address this reasoning challenge, we design two different baselines: (1) a Transformer-based method which leverages the state-of-the-art pre-trained language models and (2) Analytical Reasoning Machine (ARM), a logical-level reasoning framework extracting symbolic knowledge (e.g, participants, facts, logical functions) to deduce legitimate solutions. In our experiments, we find that the Transformer-based models struggle to solve this task as their performance is close to random guess and ARM achieves better performance by leveraging symbolic knowledge and interpretable reasoning steps. Results show that both methods still lag far behind human performance, which leave further space for future research.

Decision making demands intricate interplay between perception, memory, and reasoning to discern optimal policies. Conventional approaches to decision making face challenges related to low sample efficiency and poor generalization. In contrast, foundation models in language and vision have showcased rapid adaptation to diverse new tasks. Therefore, we advocate for the construction of foundation agents as a transformative shift in the learning paradigm of agents. This proposal is underpinned by the formulation of foundation agents with their fundamental characteristics and challenges motivated by the success of large language models (LLMs). Moreover, we specify the roadmap of foundation agents from large interactive data collection or generation, to self-supervised pretraining and adaptation, and knowledge and value alignment with LLMs. Lastly, we pinpoint critical research questions derived from the formulation and delineate trends for foundation agents supported by real-world use cases, addressing both technical and theoretical aspects to propel the field towards a more comprehensive and impactful future.

We investigate the logical reasoning capabilities of large language models (LLMs) and their scalability in complex non-monotonic reasoning. To this end, we introduce ZebraLogic, a comprehensive evaluation framework for assessing LLM reasoning performance on logic grid puzzles derived from constraint satisfaction problems (CSPs). ZebraLogic enables the generation of puzzles with controllable and quantifiable complexity, facilitating a systematic study of the scaling limits of models such as Llama, o1 models, and DeepSeek-R1. By encompassing a broad range of search space complexities and diverse logical constraints, ZebraLogic provides a structured environment to evaluate reasoning under increasing difficulty. Our results reveal a significant decline in accuracy as problem complexity grows -- a phenomenon we term the curse of complexity. This limitation persists even with larger models and increased inference-time computation, suggesting inherent constraints in current LLM reasoning capabilities. Additionally, we explore strategies to enhance logical reasoning, including Best-of-N sampling, backtracking mechanisms, and self-verification prompts. Our findings offer critical insights into the scalability of LLM reasoning, highlight fundamental limitations, and outline potential directions for improvement.