Daily Papers

High-resolution Large Multimodal Models (LMMs) encounter the challenges of excessive visual tokens and quadratic visual complexity. Current high-resolution LMMs address the quadratic complexity while still generating excessive visual tokens. However, the redundancy in visual tokens is the key problem as it leads to more substantial compute. To mitigate this issue, we propose ConvLLaVA, which employs ConvNeXt, a hierarchical backbone, as the visual encoder of LMM to replace Vision Transformer (ViT). ConvLLaVA compresses high-resolution images into information-rich visual features, effectively preventing the generation of excessive visual tokens. To enhance the capabilities of ConvLLaVA, we propose two critical optimizations. Since the low-resolution pretrained ConvNeXt underperforms when directly applied on high resolution, we update it to bridge the gap. Moreover, since ConvNeXt's original compression ratio is inadequate for much higher resolution inputs, we train a successive stage to further compress the visual tokens, thereby reducing redundancy. These optimizations enable ConvLLaVA to support inputs of 1536x1536 resolution generating only 576 visual tokens, capable of handling images of arbitrary aspect ratios. Experimental results demonstrate that our method achieves competitive performance with state-of-the-art models on mainstream benchmarks. The ConvLLaVA model series are publicly available at https://github.com/alibaba/conv-llava.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

While originally designed for natural language processing tasks, the self-attention mechanism has recently taken various computer vision areas by storm. However, the 2D nature of images brings three challenges for applying self-attention in computer vision. (1) Treating images as 1D sequences neglects their 2D structures. (2) The quadratic complexity is too expensive for high-resolution images. (3) It only captures spatial adaptability but ignores channel adaptability. In this paper, we propose a novel linear attention named large kernel attention (LKA) to enable self-adaptive and long-range correlations in self-attention while avoiding its shortcomings. Furthermore, we present a neural network based on LKA, namely Visual Attention Network (VAN). While extremely simple, VAN surpasses similar size vision transformers(ViTs) and convolutional neural networks(CNNs) in various tasks, including image classification, object detection, semantic segmentation, panoptic segmentation, pose estimation, etc. For example, VAN-B6 achieves 87.8% accuracy on ImageNet benchmark and set new state-of-the-art performance (58.2 PQ) for panoptic segmentation. Besides, VAN-B2 surpasses Swin-T 4% mIoU (50.1 vs. 46.1) for semantic segmentation on ADE20K benchmark, 2.6% AP (48.8 vs. 46.2) for object detection on COCO dataset. It provides a novel method and a simple yet strong baseline for the community. Code is available at https://github.com/Visual-Attention-Network.

In visual generation, the quadratic complexity of attention mechanisms results in high memory and computational costs, especially for longer token sequences required in high-resolution image or multi-frame video generation. To address this, prior research has explored techniques such as sparsification and quantization. However, these techniques face significant challenges under low density and reduced bitwidths. Through systematic analysis, we identify that the core difficulty stems from the dispersed and irregular characteristics of visual attention patterns. Therefore, instead of introducing specialized sparsification and quantization design to accommodate such patterns, we propose an alternative strategy: *reorganizing* the attention pattern to alleviate the challenges. Inspired by the local aggregation nature of visual feature extraction, we design a novel **Pattern-Aware token ReOrdering (PARO)** technique, which unifies the diverse attention patterns into a hardware-friendly block-wise pattern. This unification substantially simplifies and enhances both sparsification and quantization. We evaluate the performance-efficiency trade-offs of various design choices and finalize a methodology tailored for the unified pattern. Our approach, **PAROAttention**, achieves video and image generation with lossless metrics, and nearly identical results from full-precision (FP) baselines, while operating at notably lower density (~20%-30%) and bitwidth (**INT8/INT4**), achieving a **1.9x** to **2.7x** end-to-end latency speedup.

State space models (SSMs) with selection mechanisms and hardware-aware architectures, namely Mamba, have recently demonstrated significant promise in long-sequence modeling. Since the self-attention mechanism in transformers has quadratic complexity with image size and increasing computational demands, the researchers are now exploring how to adapt Mamba for computer vision tasks. This paper is the first comprehensive survey aiming to provide an in-depth analysis of Mamba models in the field of computer vision. It begins by exploring the foundational concepts contributing to Mamba's success, including the state space model framework, selection mechanisms, and hardware-aware design. Next, we review these vision mamba models by categorizing them into foundational ones and enhancing them with techniques such as convolution, recurrence, and attention to improve their sophistication. We further delve into the widespread applications of Mamba in vision tasks, which include their use as a backbone in various levels of vision processing. This encompasses general visual tasks, Medical visual tasks (e.g., 2D / 3D segmentation, classification, and image registration, etc.), and Remote Sensing visual tasks. We specially introduce general visual tasks from two levels: High/Mid-level vision (e.g., Object detection, Segmentation, Video classification, etc.) and Low-level vision (e.g., Image super-resolution, Image restoration, Visual generation, etc.). We hope this endeavor will spark additional interest within the community to address current challenges and further apply Mamba models in computer vision.

Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) stand as the two most popular foundation models for visual representation learning. While CNNs exhibit remarkable scalability with linear complexity w.r.t. image resolution, ViTs surpass them in fitting capabilities despite contending with quadratic complexity. A closer inspection reveals that ViTs achieve superior visual modeling performance through the incorporation of global receptive fields and dynamic weights. This observation motivates us to propose a novel architecture that inherits these components while enhancing computational efficiency. To this end, we draw inspiration from the recently introduced state space model and propose the Visual State Space Model (VMamba), which achieves linear complexity without sacrificing global receptive fields. To address the encountered direction-sensitive issue, we introduce the Cross-Scan Module (CSM) to traverse the spatial domain and convert any non-causal visual image into order patch sequences. Extensive experimental results substantiate that VMamba not only demonstrates promising capabilities across various visual perception tasks, but also exhibits more pronounced advantages over established benchmarks as the image resolution increases. Source code has been available at https://github.com/MzeroMiko/VMamba.

Vision Transformers (ViT) have emerged as the de-facto choice for numerous industry grade vision solutions. But their inference cost can be prohibitive for many settings, as they compute self-attention in each layer which suffers from quadratic computational complexity in the number of tokens. On the other hand, spatial information in images and spatio-temporal information in videos is usually sparse and redundant. In this work, we introduce LookupViT, that aims to exploit this information sparsity to reduce ViT inference cost. LookupViT provides a novel general purpose vision transformer block that operates by compressing information from higher resolution tokens to a fixed number of tokens. These few compressed tokens undergo meticulous processing, while the higher-resolution tokens are passed through computationally cheaper layers. Information sharing between these two token sets is enabled through a bidirectional cross-attention mechanism. The approach offers multiple advantages - (a) easy to implement on standard ML accelerators (GPUs/TPUs) via standard high-level operators, (b) applicable to standard ViT and its variants, thus generalizes to various tasks, (c) can handle different tokenization and attention approaches. LookupViT also offers flexibility for the compressed tokens, enabling performance-computation trade-offs in a single trained model. We show LookupViT's effectiveness on multiple domains - (a) for image-classification (ImageNet-1K and ImageNet-21K), (b) video classification (Kinetics400 and Something-Something V2), (c) image captioning (COCO-Captions) with a frozen encoder. LookupViT provides 2times reduction in FLOPs while upholding or improving accuracy across these domains. In addition, LookupViT also demonstrates out-of-the-box robustness and generalization on image classification (ImageNet-C,R,A,O), improving by up to 4% over ViT.

Previous research on lightweight models has primarily focused on CNNs and Transformer-based designs. CNNs, with their local receptive fields, struggle to capture long-range dependencies, while Transformers, despite their global modeling capabilities, are limited by quadratic computational complexity in high-resolution scenarios. Recently, state-space models have gained popularity in the visual domain due to their linear computational complexity. Despite their low FLOPs, current lightweight Mamba-based models exhibit suboptimal throughput. In this work, we propose the MobileMamba framework, which balances efficiency and performance. We design a three-stage network to enhance inference speed significantly. At a fine-grained level, we introduce the Multi-Receptive Field Feature Interaction(MRFFI) module, comprising the Long-Range Wavelet Transform-Enhanced Mamba(WTE-Mamba), Efficient Multi-Kernel Depthwise Convolution(MK-DeConv), and Eliminate Redundant Identity components. This module integrates multi-receptive field information and enhances high-frequency detail extraction. Additionally, we employ training and testing strategies to further improve performance and efficiency. MobileMamba achieves up to 83.6% on Top-1, surpassing existing state-of-the-art methods which is maximum x21 faster than LocalVim on GPU. Extensive experiments on high-resolution downstream tasks demonstrate that MobileMamba surpasses current efficient models, achieving an optimal balance between speed and accuracy.

Despite the significant achievements of Vision Transformers (ViTs) in various vision tasks, they are constrained by the quadratic complexity. Recently, State Space Models (SSMs) have garnered widespread attention due to their global receptive field and linear complexity with respect to the input length, demonstrating substantial potential across fields including natural language processing and computer vision. To improve the performance of SSMs in vision tasks, a multi-scan strategy is widely adopted, which leads to significant redundancy of SSMs. For a better trade-off between efficiency and performance, we analyze the underlying reasons behind the success of the multi-scan strategy, where long-range dependency plays an important role. Based on the analysis, we introduce Multi-Scale Vision Mamba (MSVMamba) to preserve the superiority of SSMs in vision tasks with limited parameters. It employs a multi-scale 2D scanning technique on both original and downsampled feature maps, which not only benefits long-range dependency learning but also reduces computational costs. Additionally, we integrate a Convolutional Feed-Forward Network (ConvFFN) to address the lack of channel mixing. Our experiments demonstrate that MSVMamba is highly competitive, with the MSVMamba-Tiny model achieving 82.8% top-1 accuracy on ImageNet, 46.9% box mAP, and 42.2% instance mAP with the Mask R-CNN framework, 1x training schedule on COCO, and 47.6% mIoU with single-scale testing on ADE20K.Code is available at https://github.com/YuHengsss/MSVMamba.

Multimodal transformer exhibits high capacity and flexibility to align image and text for visual grounding. However, the existing encoder-only grounding framework (e.g., TransVG) suffers from heavy computation due to the self-attention operation with quadratic time complexity. To address this issue, we present a new multimodal transformer architecture, coined as Dynamic Mutilmodal DETR (Dynamic MDETR), by decoupling the whole grounding process into encoding and decoding phases. The key observation is that there exists high spatial redundancy in images. Thus, we devise a new dynamic multimodal transformer decoder by exploiting this sparsity prior to speed up the visual grounding process. Specifically, our dynamic decoder is composed of a 2D adaptive sampling module and a text guided decoding module. The sampling module aims to select these informative patches by predicting the offsets with respect to a reference point, while the decoding module works for extracting the grounded object information by performing cross attention between image features and text features. These two modules are stacked alternatively to gradually bridge the modality gap and iteratively refine the reference point of grounded object, eventually realizing the objective of visual grounding. Extensive experiments on five benchmarks demonstrate that our proposed Dynamic MDETR achieves competitive trade-offs between computation and accuracy. Notably, using only 9% feature points in the decoder, we can reduce ~44% GFLOPs of the multimodal transformer, but still get higher accuracy than the encoder-only counterpart. In addition, to verify its generalization ability and scale up our Dynamic MDETR, we build the first one-stage CLIP empowered visual grounding framework, and achieve the state-of-the-art performance on these benchmarks.

While diffusion models excel at generating high-quality images from text prompts, they struggle with visual consistency in image sequences. Existing methods generate each image independently, leading to disjointed narratives - a challenge further exacerbated in non-linear storytelling, where scenes must connect beyond adjacent frames. We introduce a novel beam search strategy for latent space exploration, enabling conditional generation of full image sequences with beam search decoding. Unlike prior approaches that use fixed latent priors, our method dynamically searches for an optimal sequence of latent representations, ensuring coherent visual transitions. To address beam search's quadratic complexity, we integrate a cross-attention mechanism that efficiently scores search paths and enables pruning, prioritizing alignment with both textual prompts and visual context. Human evaluations confirm that our approach outperforms baseline methods, producing full sequences with superior coherence, visual continuity, and textual alignment. By bridging advances in search optimization and latent space refinement, this work sets a new standard for structured image sequence generation.

Recent advancements in unified multimodal understanding and visual generation (or multimodal generation) models have been hindered by their quadratic computational complexity and dependence on large-scale training data. We present OmniMamba, the first linear-architecture-based multimodal generation model that generates both text and images through a unified next-token prediction paradigm. The model fully leverages Mamba-2's high computational and memory efficiency, extending its capabilities from text generation to multimodal generation. To address the data inefficiency of existing unified models, we propose two key innovations: (1) decoupled vocabularies to guide modality-specific generation, and (2) task-specific LoRA for parameter-efficient adaptation. Furthermore, we introduce a decoupled two-stage training strategy to mitigate data imbalance between two tasks. Equipped with these techniques, OmniMamba achieves competitive performance with JanusFlow while surpassing Show-o across benchmarks, despite being trained on merely 2M image-text pairs, which is 1,000 times fewer than Show-o. Notably, OmniMamba stands out with outstanding inference efficiency, achieving up to a 119.2 times speedup and 63% GPU memory reduction for long-sequence generation compared to Transformer-based counterparts. Code and models are released at https://github.com/hustvl/OmniMamba

Self-attention-based vision transformers (ViTs) have emerged as a highly competitive architecture in computer vision. Unlike convolutional neural networks (CNNs), ViTs are capable of global information sharing. With the development of various structures of ViTs, ViTs are increasingly advantageous for many vision tasks. However, the quadratic complexity of self-attention renders ViTs computationally intensive, and their lack of inductive biases of locality and translation equivariance demands larger model sizes compared to CNNs to effectively learn visual features. In this paper, we propose a light-weight and efficient vision transformer model called DualToken-ViT that leverages the advantages of CNNs and ViTs. DualToken-ViT effectively fuses the token with local information obtained by convolution-based structure and the token with global information obtained by self-attention-based structure to achieve an efficient attention structure. In addition, we use position-aware global tokens throughout all stages to enrich the global information, which further strengthening the effect of DualToken-ViT. Position-aware global tokens also contain the position information of the image, which makes our model better for vision tasks. We conducted extensive experiments on image classification, object detection and semantic segmentation tasks to demonstrate the effectiveness of DualToken-ViT. On the ImageNet-1K dataset, our models of different scales achieve accuracies of 75.4% and 79.4% with only 0.5G and 1.0G FLOPs, respectively, and our model with 1.0G FLOPs outperforms LightViT-T using global tokens by 0.7%.

Contemporary diffusion models built upon U-Net or Diffusion Transformer (DiT) architectures have revolutionized image generation through transformer-based attention mechanisms. The prevailing paradigm has commonly employed self-attention with quadratic computational complexity to handle global spatial relationships in complex images, thereby synthesizing high-fidelity images with coherent visual semantics.Contrary to conventional wisdom, our systematic layer-wise analysis reveals an interesting discrepancy: self-attention in pre-trained diffusion models predominantly exhibits localized attention patterns, closely resembling convolutional inductive biases. This suggests that global interactions in self-attention may be less critical than commonly assumed.Driven by this, we propose \(\Delta\)ConvFusion to replace conventional self-attention modules with Pyramid Convolution Blocks (\(\Delta\)ConvBlocks).By distilling attention patterns into localized convolutional operations while keeping other components frozen, \(\Delta\)ConvFusion achieves performance comparable to transformer-based counterparts while reducing computational cost by 6929times and surpassing LinFusion by 5.42times in efficiency--all without compromising generative fidelity.

Modern diffusion models, particularly those utilizing a Transformer-based UNet for denoising, rely heavily on self-attention operations to manage complex spatial relationships, thus achieving impressive generation performance. However, this existing paradigm faces significant challenges in generating high-resolution visual content due to its quadratic time and memory complexity with respect to the number of spatial tokens. To address this limitation, we aim at a novel linear attention mechanism as an alternative in this paper. Specifically, we begin our exploration from recently introduced models with linear complexity, e.g., Mamba, Mamba2, and Gated Linear Attention, and identify two key features-attention normalization and non-causal inference-that enhance high-resolution visual generation performance. Building on these insights, we introduce a generalized linear attention paradigm, which serves as a low-rank approximation of a wide spectrum of popular linear token mixers. To save the training cost and better leverage pre-trained models, we initialize our models and distill the knowledge from pre-trained StableDiffusion (SD). We find that the distilled model, termed LinFusion, achieves performance on par with or superior to the original SD after only modest training, while significantly reducing time and memory complexity. Extensive experiments on SD-v1.5, SD-v2.1, and SD-XL demonstrate that LinFusion delivers satisfactory zero-shot cross-resolution generation performance, generating high-resolution images like 16K resolution. Moreover, it is highly compatible with pre-trained SD components, such as ControlNet and IP-Adapter, requiring no adaptation efforts. Codes are available at https://github.com/Huage001/LinFusion.

This paper presents innovative enhancements to diffusion models by integrating a novel multi-resolution network and time-dependent layer normalization. Diffusion models have gained prominence for their effectiveness in high-fidelity image generation. While conventional approaches rely on convolutional U-Net architectures, recent Transformer-based designs have demonstrated superior performance and scalability. However, Transformer architectures, which tokenize input data (via "patchification"), face a trade-off between visual fidelity and computational complexity due to the quadratic nature of self-attention operations concerning token length. While larger patch sizes enable attention computation efficiency, they struggle to capture fine-grained visual details, leading to image distortions. To address this challenge, we propose augmenting the Diffusion model with the Multi-Resolution network (DiMR), a framework that refines features across multiple resolutions, progressively enhancing detail from low to high resolution. Additionally, we introduce Time-Dependent Layer Normalization (TD-LN), a parameter-efficient approach that incorporates time-dependent parameters into layer normalization to inject time information and achieve superior performance. Our method's efficacy is demonstrated on the class-conditional ImageNet generation benchmark, where DiMR-XL variants outperform prior diffusion models, setting new state-of-the-art FID scores of 1.70 on ImageNet 256 x 256 and 2.89 on ImageNet 512 x 512. Project page: https://qihao067.github.io/projects/DiMR

Understanding how humans perceive visual complexity is a key area of study in visual cognition. Previous approaches to modeling visual complexity assessments have often resulted in intricate, difficult-to-interpret algorithms that employ numerous features or sophisticated deep learning architectures. While these complex models achieve high performance on specific datasets, they often sacrifice interpretability, making it challenging to understand the factors driving human perception of complexity. Recently (Shen, et al. 2024) proposed an interpretable segmentation-based model that accurately predicted complexity across various datasets, supporting the idea that complexity can be explained simply. In this work, we investigate the failure of their model to capture structural, color and surprisal contributions to complexity. To this end, we propose Multi-Scale Sobel Gradient (MSG) which measures spatial intensity variations, Multi-Scale Unique Color (MUC) which quantifies colorfulness across multiple scales, and surprise scores generated using a Large Language Model. We test our features on existing benchmarks and a novel dataset (Surprising Visual Genome) containing surprising images from Visual Genome. Our experiments demonstrate that modeling complexity accurately is not as simple as previously thought, requiring additional perceptual and semantic factors to address dataset biases. Our model improves predictive performance while maintaining interpretability, offering deeper insights into how visual complexity is perceived and assessed. Our code, analysis and data are available at https://github.com/Complexity-Project/Complexity-in-Complexity.

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear complexity by approximating the Softmax operation through carefully designed mapping functions. However, current linear attention approaches either suffer from significant performance degradation or introduce additional computation overhead from the mapping functions. In this paper, we propose a novel Focused Linear Attention module to achieve both high efficiency and expressiveness. Specifically, we first analyze the factors contributing to the performance degradation of linear attention from two perspectives: the focus ability and feature diversity. To overcome these limitations, we introduce a simple yet effective mapping function and an efficient rank restoration module to enhance the expressiveness of self-attention while maintaining low computation complexity. Extensive experiments show that our linear attention module is applicable to a variety of advanced vision Transformers, and achieves consistently improved performances on multiple benchmarks. Code is available at https://github.com/LeapLabTHU/FLatten-Transformer.

Recent studies suggest that deep learning models inductive bias towards favoring simpler features may be one of the sources of shortcut learning. Yet, there has been limited focus on understanding the complexity of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features, represented as directions in the penultimate layer, that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity and find a spectrum of simple to complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features flow, and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features complexity and their importance in driving the networks decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a sedimentation process, allowing the model to build upon these foundational elements.

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the complexity of concepts becomes diverse. Specifically, at the representational level, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the computational level, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.

Transformers have been successful in many vision tasks, thanks to their capability of capturing long-range dependency. However, their quadratic computational complexity poses a major obstacle for applying them to vision tasks requiring dense predictions, such as object detection, feature matching, stereo, etc. We introduce QuadTree Attention, which reduces the computational complexity from quadratic to linear. Our quadtree transformer builds token pyramids and computes attention in a coarse-to-fine manner. At each level, the top K patches with the highest attention scores are selected, such that at the next level, attention is only evaluated within the relevant regions corresponding to these top K patches. We demonstrate that quadtree attention achieves state-of-the-art performance in various vision tasks, e.g. with 4.0% improvement in feature matching on ScanNet, about 50% flops reduction in stereo matching, 0.4-1.5% improvement in top-1 accuracy on ImageNet classification, 1.2-1.8% improvement on COCO object detection, and 0.7-2.4% improvement on semantic segmentation over previous state-of-the-art transformers. The codes are available at https://github.com/Tangshitao/QuadtreeAttention.

Recent advancements in Large Multimodal Models (LMMs) have shown promising results in mathematical reasoning within visual contexts, with models approaching human-level performance on existing benchmarks such as MathVista. However, we observe significant limitations in the diversity of questions and breadth of subjects covered by these benchmarks. To address this issue, we present the MATH-Vision (MATH-V) dataset, a meticulously curated collection of 3,040 high-quality mathematical problems with visual contexts sourced from real math competitions. Spanning 16 distinct mathematical disciplines and graded across 5 levels of difficulty, our dataset provides a comprehensive and diverse set of challenges for evaluating the mathematical reasoning abilities of LMMs. Through extensive experimentation, we unveil a notable performance gap between current LMMs and human performance on MATH-V, underscoring the imperative for further advancements in LMMs. Moreover, our detailed categorization allows for a thorough error analysis of LMMs, offering valuable insights to guide future research and development. The project is available at https://mathvision-cuhk.github.io

The quadratic computational complexity in the self-attention mechanism of popular transformer architectures poses significant challenges for training and inference, particularly in terms of efficiency and memory requirements. Towards addressing these challenges, this paper introduces a novel fast computation method for gradient calculation in multi-layer transformer models. Our approach enables the computation of gradients for the entire multi-layer transformer model in almost linear time n^{1+o(1)}, where n is the input sequence length. This breakthrough significantly reduces the computational bottleneck associated with the traditional quadratic time complexity. Our theory holds for any loss function and maintains a bounded approximation error across the entire model. Furthermore, our analysis can hold when the multi-layer transformer model contains many practical sub-modules, such as residual connection, casual mask, and multi-head attention. By improving the efficiency of gradient computation in large language models, we hope that our work will facilitate the more effective training and deployment of long-context language models based on our theoretical results.

Vision language models (VLMs) achieve unified modeling of images and text, enabling them to accomplish complex real-world tasks through perception, planning, and reasoning. Among these tasks, reasoning is particularly representative, with mathematical reasoning serving as a prominent example. It highlights the high-level capability of VLMs to comprehend mathematical information in images and to perform sophisticated reasoning. Recently, numerous visual mathematical reasoning benchmarks have been proposed, but they are often restricted to geometry, lack coverage of math word problems, and rarely assess reasoning across multiple images. To address these gaps, we introduce GSM8K-V, a purely visual multi-image mathematical reasoning benchmark. GSM8K-V is built by systematically mapping each sample from the widely used text-based GSM8K into visual form. Through a carefully designed automated image-generation pipeline combined with meticulous human annotation, we curate 1,319 high-quality samples. We evaluate a wide range of open-source and closed-source models on GSM8K-V. Results show that although existing VLMs have nearly saturated performance on text-based GSM8K, there remains substantial room for improvement on GSM8K-V. For example, the best-performing model, Gemini-2.5-Pro, achieves 95.22% accuracy on GSM8K but only 46.93% on GSM8K-V. We conduct a comprehensive analysis of GSM8K-V, examining the limitations of current models as well as potential directions for improvement. GSM8K-V offers a new perspective on visual mathematical reasoning and establishes a benchmark to guide the development of more robust and generalizable VLMs.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

Transformer-based video diffusion models (VDMs) deliver state-of-the-art video generation quality but are constrained by the quadratic cost of self-attention, making long sequences and high resolutions computationally expensive. While linear attention offers sub-quadratic complexity, prior attempts fail to match the expressiveness of softmax attention without costly retraining. We introduce Attention Surgery, an efficient framework for linearizing or hybridizing attention in pretrained VDMs without training from scratch. Inspired by recent advances in language models, our method combines a novel hybrid attention mechanism-mixing softmax and linear tokens-with a lightweight distillation and fine-tuning pipeline requiring only a few GPU-days. Additionally, we incorporate a cost-aware block-rate strategy to balance expressiveness and efficiency across layers. Applied to Wan2.1 1.3B, a state-of-the-art DiT-based VDM, Attention Surgery achieves the first competitive sub-quadratic attention video diffusion models, reducing attention cost by up to 40\% in terms of FLOPs, while maintaining generation quality as measured on the standard VBench and VBench-2.0 benchmarks.

Vision-Language Models (VLMs) have demonstrated remarkable success across diverse visual tasks, yet their performance degrades in complex visual environments. While existing enhancement approaches require additional training, rely on external segmentation tools, or operate at coarse-grained levels, they overlook the innate ability within VLMs. To bridge this gap, we investigate VLMs' attention patterns and discover that: (1) visual complexity strongly correlates with attention entropy, negatively impacting reasoning performance; (2) attention progressively refines from global scanning in shallow layers to focused convergence in deeper layers, with convergence degree determined by visual complexity. (3) Theoretically, we prove that the contrast of attention maps between general queries and task-specific queries enables the decomposition of visual signal into semantic signals and visual noise components. Building on these insights, we propose Contrastive Attention Refinement for Visual Enhancement (CARVE), a training-free method that extracts task-relevant visual signals through attention contrasting at the pixel level. Extensive experiments demonstrate that CARVE consistently enhances performance, achieving up to 75% improvement on open-source models. Our work provides critical insights into the interplay between visual complexity and attention mechanisms, offering an efficient pathway for improving visual reasoning with contrasting attention.

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form h = g circ p where p : R^d rightarrow R is a degree k polynomial and g: R rightarrow R is a degree q polynomial. This function class generalizes the single-index model, which corresponds to k=1, and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree k polynomials p, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target h up to vanishing test error in mathcal{O}(d^k) samples and polynomial time. This is a strict improvement over kernel methods, which require widetilde Theta(d^{kq}) samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of p being a quadratic. When p is indeed a quadratic, we achieve the information-theoretically optimal sample complexity mathcal{O}(d^2), which is an improvement over prior work~nichani2023provable requiring a sample size of widetildeTheta(d^4). Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature p with mathcal{O}(d^k) samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions.

We introduce KiloGram, a resource for studying abstract visual reasoning in humans and machines. Drawing on the history of tangram puzzles as stimuli in cognitive science, we build a richly annotated dataset that, with >1k distinct stimuli, is orders of magnitude larger and more diverse than prior resources. It is both visually and linguistically richer, moving beyond whole shape descriptions to include segmentation maps and part labels. We use this resource to evaluate the abstract visual reasoning capacities of recent multi-modal models. We observe that pre-trained weights demonstrate limited abstract reasoning, which dramatically improves with fine-tuning. We also observe that explicitly describing parts aids abstract reasoning for both humans and models, especially when jointly encoding the linguistic and visual inputs. KiloGram is available at https://lil.nlp.cornell.edu/kilogram .

Recent advancements in Large Vision-Language Models (LVLMs) have significantly enhanced their ability to integrate visual and linguistic information, achieving near-human proficiency in tasks like object recognition, captioning, and visual question answering. However, current benchmarks typically focus on knowledge-centric evaluations that assess domain-specific expertise, often neglecting the core ability to reason about fundamental mathematical elements and visual concepts. We identify a gap in evaluating elementary-level math problems, which rely on explicit visual dependencies-requiring models to discern, integrate, and reason across multiple images while incorporating commonsense knowledge, all of which are crucial for advancing toward broader AGI capabilities. To address this gap, we introduce VCBENCH, a comprehensive benchmark for multimodal mathematical reasoning with explicit visual dependencies. VCBENCH includes 1,720 problems across six cognitive domains, featuring 6,697 images (averaging 3.9 per question) to ensure multi-image reasoning. We evaluate 26 state-of-the-art LVLMs on VCBENCH, revealing substantial performance disparities, with even the top models unable to exceed 50% accuracy. Our findings highlight the ongoing challenges in visual-mathematical integration and suggest avenues for future LVLM advancements.

Recently, large language and vision models (LLVMs) have received significant attention and development efforts due to their remarkable generalization performance across a wide range of tasks requiring perception and cognitive abilities. A key factor behind their success is their simple architecture, which consists of a vision encoder, a projector, and a large language model (LLM). Despite their achievements in advanced reasoning tasks, their performance on fundamental perception-related tasks (e.g., MMVP) remains surprisingly low. This discrepancy raises the question of how LLVMs truly perceive images and exploit the advantages of the vision encoder. To address this, we systematically investigate this question regarding several aspects: permutation invariance, robustness, math reasoning, alignment preserving and importance, by evaluating the most common LLVM's families (i.e., LLaVA) across 10 evaluation benchmarks. Our extensive experiments reveal several intriguing properties of current LLVMs: (1) they internally process the image in a global manner, even when the order of visual patch sequences is randomly permuted; (2) they are sometimes able to solve math problems without fully perceiving detailed numerical information; (3) the cross-modal alignment is overfitted to complex reasoning tasks, thereby, causing them to lose some of the original perceptual capabilities of their vision encoder; (4) the representation space in the lower layers (<25%) plays a crucial role in determining performance and enhancing visual understanding. Lastly, based on the above observations, we suggest potential future directions for building better LLVMs and constructing more challenging evaluation benchmarks.

Mathematical reasoning is critical for tasks such as precise distance and area computations, trajectory estimations, and spatial analysis in unmanned aerial vehicle (UAV) based remote sensing, yet current vision-language models (VLMs) have not been adequately tested in this domain. To address this gap, we introduce AVI-Math, the first benchmark to rigorously evaluate multimodal mathematical reasoning in aerial vehicle imagery, moving beyond simple counting tasks to include domain-specific knowledge in areas such as geometry, logic, and algebra. The dataset comprises 3,773 high-quality vehicle-related questions captured from UAV views, covering 6 mathematical subjects and 20 topics. The data, collected at varying altitudes and from multiple UAV angles, reflects real-world UAV scenarios, ensuring the diversity and complexity of the constructed mathematical problems. In this paper, we benchmark 14 prominent VLMs through a comprehensive evaluation and demonstrate that, despite their success on previous multimodal benchmarks, these models struggle with the reasoning tasks in AVI-Math. Our detailed analysis highlights significant limitations in the mathematical reasoning capabilities of current VLMs and suggests avenues for future research. Furthermore, we explore the use of Chain-of-Thought prompting and fine-tuning techniques, which show promise in addressing the reasoning challenges in AVI-Math. Our findings not only expose the limitations of VLMs in mathematical reasoning but also offer valuable insights for advancing UAV-based trustworthy VLMs in real-world applications. The code, and datasets will be released at https://github.com/VisionXLab/avi-math

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

Vision transformers (ViTs) have pushed the state-of-the-art for visual perception tasks. The self-attention mechanism underpinning the strength of ViTs has a quadratic complexity in both computation and memory usage. This motivates the development of approximating the self-attention at linear complexity. However, an in-depth analysis in this work reveals that existing methods are either theoretically flawed or empirically ineffective for visual recognition. We identify that their limitations are rooted in the inheritance of softmax-based self-attention during approximations, that is, normalizing the scaled dot-product between token feature vectors using the softmax function. As preserving the softmax operation challenges any subsequent linearization efforts. By this insight, a family of Softmax-Free Transformers (SOFT) are proposed. Specifically, a Gaussian kernel function is adopted to replace the dot-product similarity, enabling a full self-attention matrix to be approximated under low-rank matrix decomposition. For computational robustness, we estimate the Moore-Penrose inverse using an iterative Newton-Raphson method in the forward process only, while calculating its theoretical gradients only once in the backward process. To further expand applicability (e.g., dense prediction tasks), an efficient symmetric normalization technique is introduced. Extensive experiments on ImageNet, COCO, and ADE20K show that our SOFT significantly improves the computational efficiency of existing ViT variants. With linear complexity, much longer token sequences are permitted by SOFT, resulting in superior trade-off between accuracy and complexity. Code and models are available at https://github.com/fudan-zvg/SOFT.

Large multimodal models extend the impressive capabilities of large language models by integrating multimodal understanding abilities. However, it is not clear how they can emulate the general intelligence and reasoning ability of humans. As recognizing patterns and abstracting concepts are key to general intelligence, we introduce PuzzleVQA, a collection of puzzles based on abstract patterns. With this dataset, we evaluate large multimodal models with abstract patterns based on fundamental concepts, including colors, numbers, sizes, and shapes. Through our experiments on state-of-the-art large multimodal models, we find that they are not able to generalize well to simple abstract patterns. Notably, even GPT-4V cannot solve more than half of the puzzles. To diagnose the reasoning challenges in large multimodal models, we progressively guide the models with our ground truth reasoning explanations for visual perception, inductive reasoning, and deductive reasoning. Our systematic analysis finds that the main bottlenecks of GPT-4V are weaker visual perception and inductive reasoning abilities. Through this work, we hope to shed light on the limitations of large multimodal models and how they can better emulate human cognitive processes in the future (Our data and code will be released publicly at https://github.com/declare-lab/LLM-PuzzleTest).

Large language models have recently shown human level performance on a variety of reasoning tasks. However, the ability of these models to perform complex visual reasoning has not been studied in detail yet. A key challenge in many visual reasoning tasks is that the visual information needs to be tightly integrated in the reasoning process. We propose to address this challenge by drawing inspiration from human visual problem solving which depends on a variety of low-level visual capabilities. It can often be cast as the three step-process of ``Look, Remember, Reason'': visual information is incrementally extracted using low-level visual routines in a step-by-step fashion until a final answer is reached. We follow the same paradigm to enable existing large language models, with minimal changes to the architecture, to solve visual reasoning problems. To this end, we introduce rationales over the visual input that allow us to integrate low-level visual capabilities, such as object recognition and tracking, as surrogate tasks. We show competitive performance on diverse visual reasoning tasks from the CLEVR, CATER, and ACRE datasets over state-of-the-art models designed specifically for these tasks.

Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices Kin R^{ntimes n}. K's columns are indexed by a set of n keys k_1,k_2ldots, k_nin R^d, rows by a set of n queries q_1,q_2,ldots,q_nin R^d , and its i,j entry is K_{ij} = e^{-|q_i-k_j|_2^2/2sigma^2} for some bandwidth parameter sigma>0. Given a vector xin R^n and error parameter epsilon>0, our task is to output a yin R^n such that |Kx-y|_2leq epsilon |x|_2 in time subquadratic in n and linear in d. Our algorithms rely on the following modelling assumption about the matrices K: the sum of the entries of K scales linearly in n, as opposed to worst case quadratic growth. We validate this assumption experimentally, for Gaussian kernel matrices encountered in various settings such as fast attention computation in LLMs. We obtain the first subquadratic-time algorithm that works under this assumption, for unrestricted vectors.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language models in solving algorithmic puzzles that necessitate both visual understanding, language understanding, and complex algorithmic reasoning. We create the puzzles to encompass a diverse array of mathematical and algorithmic topics such as boolean logic, combinatorics, graph theory, optimization, search, etc., aiming to evaluate the gap between visual data interpretation and algorithmic problem-solving skills. The dataset is generated automatically from code authored by humans. All our puzzles have exact solutions that can be found from the algorithm without tedious human calculations. It ensures that our dataset can be scaled up arbitrarily in terms of reasoning complexity and dataset size. Our investigation reveals that large language models (LLMs) such as GPT4V and Gemini exhibit limited performance in puzzle-solving tasks. We find that their performance is near random in a multi-choice question-answering setup for a significant number of puzzles. The findings emphasize the challenges of integrating visual, language, and algorithmic knowledge for solving complex reasoning problems.

The rapid progress of image generative AI has blurred the boundary between synthetic and real images, fueling an arms race between generators and discriminators. This paper investigates the conditions under which discriminators are most disadvantaged in this competition. We analyze two key factors: data dimensionality and data complexity. While increased dimensionality often strengthens the discriminators ability to detect subtle inconsistencies, complexity introduces a more nuanced effect. Using Kolmogorov complexity as a measure of intrinsic dataset structure, we show that both very simple and highly complex datasets reduce the detectability of synthetic images; generators can learn simple datasets almost perfectly, whereas extreme diversity masks imperfections. In contrast, intermediate-complexity datasets create the most favorable conditions for detection, as generators fail to fully capture the distribution and their errors remain visible.

Video diffusion models (DMs) have enabled high-quality video synthesis. However, their computation costs scale quadratically with sequence length because self-attention has quadratic complexity. While linear attention lowers the cost, fully replacing quadratic attention requires expensive pretraining due to the limited expressiveness of linear attention and the complexity of spatiotemporal modeling in video generation. In this paper, we present LinVideo, an efficient data-free post-training framework that replaces a target number of self-attention modules with linear attention while preserving the original model's performance. First, we observe a significant disparity in the replaceability of different layers. Instead of manual or heuristic choices, we frame layer selection as a binary classification problem and propose selective transfer, which automatically and progressively converts layers to linear attention with minimal performance impact. Additionally, to overcome the ineffectiveness and inefficiency of existing objectives for this transfer process, we introduce an anytime distribution matching (ADM) objective that aligns the distributions of samples across any timestep along the sampling trajectory. This objective is efficient and recovers model performance. Extensive experiments show that our method achieves a 1.25-2.00x speedup while preserving generation quality, and our 4-step distilled model further delivers a 15.92x latency reduction with minimal visual quality drop.

Although Large Language Models (LLMs) and Large Multimodal Models (LMMs) exhibit impressive skills in various domains, their ability for mathematical reasoning within visual contexts has not been formally examined. Equipping LLMs and LMMs with this capability is vital for general-purpose AI assistants and showcases promising potential in education, data analysis, and scientific discovery. To bridge this gap, we present MathVista, a benchmark designed to amalgamate challenges from diverse mathematical and visual tasks. We first taxonomize the key task types, reasoning skills, and visual contexts from the literature to guide our selection from 28 existing math-focused and visual question answering datasets. Then, we construct three new datasets, IQTest, FunctionQA, and PaperQA, to accommodate for missing types of visual contexts. The problems featured often require deep visual understanding beyond OCR or image captioning, and compositional reasoning with rich domain-specific tools, thus posing a notable challenge to existing models. We conduct a comprehensive evaluation of 11 prominent open-source and proprietary foundation models (LLMs, LLMs augmented with tools, and LMMs), and early experiments with GPT-4V. The best-performing model, Multimodal Bard, achieves only 58% of human performance (34.8% vs 60.3%), indicating ample room for further improvement. Given this significant gap, MathVista fuels future research in the development of general-purpose AI agents capable of tackling mathematically intensive and visually rich real-world tasks. Preliminary tests show that MathVista also presents challenges to GPT-4V, underscoring the benchmark's importance. The project is available at https://mathvista.github.io/.

Although previous research on large language models (LLMs) and large multi-modal models (LMMs) has systematically explored mathematical problem-solving (MPS) within visual contexts, the analysis of how these models process visual information during problem-solving remains insufficient. To address this gap, we present VisAidMath, a benchmark for evaluating the MPS process related to visual information. We follow a rigorous data curation pipeline involving both automated processes and manual annotations to ensure data quality and reliability. Consequently, this benchmark includes 1,200 challenging problems from various mathematical branches, vision-aid formulations, and difficulty levels, collected from diverse sources such as textbooks, examination papers, and Olympiad problems. Based on the proposed benchmark, we conduct comprehensive evaluations on ten mainstream LLMs and LMMs, highlighting deficiencies in the visual-aided reasoning process. For example, GPT-4V only achieves 45.33% accuracy in the visual-aided reasoning task, even with a drop of 2 points when provided with golden visual aids. In-depth analysis reveals that the main cause of deficiencies lies in hallucination regarding the implicit visual reasoning process, shedding light on future research directions in the visual-aided MPS process.

In recent years, the application of multimodal large language models (MLLM) in various fields has achieved remarkable success. However, as the foundation model for many downstream tasks, current MLLMs are composed of the well-known Transformer network, which has a less efficient quadratic computation complexity. To improve the efficiency of such basic models, we propose Cobra, a linear computational complexity MLLM. Specifically, Cobra integrates the efficient Mamba language model into the visual modality. Moreover, we explore and study various modal fusion schemes to create an effective multi-modal Mamba. Extensive experiments demonstrate that (1) Cobra achieves extremely competitive performance with current computationally efficient state-of-the-art methods, e.g., LLaVA-Phi, TinyLLaVA, and MobileVLM v2, and has faster speed due to Cobra's linear sequential modeling. (2) Interestingly, the results of closed-set challenging prediction benchmarks show that Cobra performs well in overcoming visual illusions and spatial relationship judgments. (3) Notably, Cobra even achieves comparable performance to LLaVA with about 43% of the number of parameters. We will make all codes of Cobra open-source and hope that the proposed method can facilitate future research on complexity problems in MLLM. Our project page is available at: https://sites.google.com/view/cobravlm.

Advancing machine visual reasoning requires a deeper understanding of how Vision-Language Models (VLMs) process and interpret complex visual patterns. This work introduces a novel, cognitively-inspired evaluation framework to systematically analyze VLM reasoning on natural image-based Bongard Problems. We propose three structured paradigms -- Direct Visual Rule Learning, Deductive Rule Learning, and Componential Analysis -- designed to progressively enforce step-wise reasoning and disentangle the interplay between perception and reasoning. Our evaluation shows that advanced, closed-source VLMs (GPT-4o and Gemini 2.0) achieve near-superhuman performance, particularly when provided with high-quality image descriptions, while open-source models exhibit a significant performance bottleneck due to deficiencies in perception. An ablation study further confirms that perception, rather than reasoning, is the primary limiting factor, as open-source models apply extracted rules effectively when given accurate descriptions. These findings underscore the critical role of robust multimodal perception in enhancing generalizable visual reasoning and highlight the importance of structured, step-wise reasoning paradigms for advancing machine intelligence.

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

Compositional visual reasoning has emerged as a key research frontier in multimodal AI, aiming to endow machines with the human-like ability to decompose visual scenes, ground intermediate concepts, and perform multi-step logical inference. While early surveys focus on monolithic vision-language models or general multimodal reasoning, a dedicated synthesis of the rapidly expanding compositional visual reasoning literature is still missing. We fill this gap with a comprehensive survey spanning 2023 to 2025 that systematically reviews 260+ papers from top venues (CVPR, ICCV, NeurIPS, ICML, ACL, etc.). We first formalize core definitions and describe why compositional approaches offer advantages in cognitive alignment, semantic fidelity, robustness, interpretability, and data efficiency. Next, we trace a five-stage paradigm shift: from prompt-enhanced language-centric pipelines, through tool-enhanced LLMs and tool-enhanced VLMs, to recently minted chain-of-thought reasoning and unified agentic VLMs, highlighting their architectural designs, strengths, and limitations. We then catalog 60+ benchmarks and corresponding metrics that probe compositional visual reasoning along dimensions such as grounding accuracy, chain-of-thought faithfulness, and high-resolution perception. Drawing on these analyses, we distill key insights, identify open challenges (e.g., limitations of LLM-based reasoning, hallucination, a bias toward deductive reasoning, scalable supervision, tool integration, and benchmark limitations), and outline future directions, including world-model integration, human-AI collaborative reasoning, and richer evaluation protocols. By offering a unified taxonomy, historical roadmap, and critical outlook, this survey aims to serve as a foundational reference and inspire the next generation of compositional visual reasoning research.

Convolutional Neural Networks (CNNs) have advanced existing medical systems for automatic disease diagnosis. However, there are still concerns about the reliability of deep medical diagnosis systems against the potential threats of adversarial attacks since inaccurate diagnosis could lead to disastrous consequences in the safety realm. In this study, we propose a highly robust yet efficient CNN-Transformer hybrid model which is equipped with the locality of CNNs as well as the global connectivity of vision Transformers. To mitigate the high quadratic complexity of the self-attention mechanism while jointly attending to information in various representation subspaces, we construct our attention mechanism by means of an efficient convolution operation. Moreover, to alleviate the fragility of our Transformer model against adversarial attacks, we attempt to learn smoother decision boundaries. To this end, we augment the shape information of an image in the high-level feature space by permuting the feature mean and variance within mini-batches. With less computational complexity, our proposed hybrid model demonstrates its high robustness and generalization ability compared to the state-of-the-art studies on a large-scale collection of standardized MedMNIST-2D datasets.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ell_1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ell_1 norm is highly suboptimal compared to other functions suited to approximating ell_q with 0 leq q < 1 (including recently proposed Continuous Exact relaxations), both in terms of performance and in the production of features that are akin to signatures of the primary visual cortex. We show that ell_1 sparsity produces a denser code or employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. For all the penalty functions tested, a subset of the neurons develop orientation selectivity similarly to V1 neurons. When their code is sparse enough, the methods also develop receptive fields with varying functionalities, another signature of V1. Compared to other methods, soft thresholding achieves this level of sparsity at the expense of much degraded reconstruction performance, that more likely than not is not acceptable in biological vision. Our results indicate that V1 uses a sparsity inducing regularization that is closer to the ell_0 pseudo-norm rather than to the ell_1 norm.

Modern vision models have achieved remarkable success in benchmarks where local features provide critical information about the target. There is now a growing interest in solving tasks that require more global reasoning, where local features offer no significant information. These tasks are reminiscent of the connectivity tasks discussed by Minsky and Papert in 1969, which exposed the limitations of the perceptron model and contributed to the first AI winter. In this paper, we revisit such tasks by introducing four global visual benchmarks involving path findings and mazes. We show that: (1) although today's large vision models largely surpass the expressivity limitations of the early models, they still struggle with the learning efficiency; we put forward the "globality degree" notion to understand this limitation; (2) we then demonstrate that the picture changes and global reasoning becomes feasible with the introduction of "visual scratchpads"; similarly to the text scratchpads and chain-of-thoughts used in language models, visual scratchpads help break down global tasks into simpler ones; (3) we finally show that some scratchpads are better than others, in particular, "inductive scratchpads" that take steps relying on less information afford better out-of-distribution generalization and succeed for smaller model sizes.

Self-attention has become a defacto choice for capturing global context in various vision applications. However, its quadratic computational complexity with respect to image resolution limits its use in real-time applications, especially for deployment on resource-constrained mobile devices. Although hybrid approaches have been proposed to combine the advantages of convolutions and self-attention for a better speed-accuracy trade-off, the expensive matrix multiplication operations in self-attention remain a bottleneck. In this work, we introduce a novel efficient additive attention mechanism that effectively replaces the quadratic matrix multiplication operations with linear element-wise multiplications. Our design shows that the key-value interaction can be replaced with a linear layer without sacrificing any accuracy. Unlike previous state-of-the-art methods, our efficient formulation of self-attention enables its usage at all stages of the network. Using our proposed efficient additive attention, we build a series of models called "SwiftFormer" which achieves state-of-the-art performance in terms of both accuracy and mobile inference speed. Our small variant achieves 78.5% top-1 ImageNet-1K accuracy with only 0.8 ms latency on iPhone 14, which is more accurate and 2x faster compared to MobileViT-v2. Code: https://github.com/Amshaker/SwiftFormer

Despite the rapid progress of multimodal large language models (MLLMs), they have largely overlooked the importance of visual processing. In a simple yet revealing experiment, we interestingly find that language-only models, when provided with image captions, can achieve comparable or even better performance than MLLMs that consume raw visual inputs. This suggests that current MLLMs may generate accurate visual descriptions but fail to effectively integrate them during reasoning. Motivated by this, we propose a simple visual perturbation framework that enhances perceptual robustness without requiring algorithmic modifications or additional training data. Our approach introduces three targeted perturbations: distractor concatenation, dominance-preserving mixup, and random rotation, that can be easily integrated into existing post-training pipelines including SFT, DPO, and GRPO. Through extensive experiments across multiple datasets, we demonstrate consistent improvements in mathematical reasoning performance, with gains comparable to those achieved through algorithmic changes. Additionally, we achieve competitive performance among open-source 7B RL-tuned models by training Qwen2.5-VL-7B with visual perturbation. Through comprehensive ablation studies, we analyze the effectiveness of different perturbation strategies, revealing that each perturbation type contributes uniquely to different aspects of visual reasoning. Our findings highlight the critical role of visual perturbation in multimodal mathematical reasoning: better reasoning begins with better seeing. Our code is available at https://github.com/YutingLi0606/Vision-Matters.

We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at the pixel-level, and solved at inference-time, that can capture global and local image characteristics. The distance in embedding space is used to define a perceptual similarity metric which we call LASI: Linear Autoregressive Similarity Index. Experiments on full-reference image quality assessment datasets show LASI performs competitively with learned deep feature based methods like LPIPS (Zhang et al., 2018) and PIM (Bhardwaj et al., 2020), at a similar computational cost to hand-crafted methods such as MS-SSIM (Wang et al., 2003). We found that increasing the dimensionality of the embedding space consistently reduces the WLS loss while increasing performance on perceptual tasks, at the cost of increasing the computational complexity. LASI is fully differentiable, scales cubically with the number of embedding dimensions, and can be parallelized at the pixel-level. A Maximum Differentiation (MAD) competition (Wang & Simoncelli, 2008) between LASI and LPIPS shows that both methods are capable of finding failure points for the other, suggesting these metrics can be combined.

Most advanced visual grounding methods rely on Transformers for visual-linguistic feature fusion. However, these Transformer-based approaches encounter a significant drawback: the computational costs escalate quadratically due to the self-attention mechanism in the Transformer Encoder, particularly when dealing with high-resolution images or long context sentences. This quadratic increase in computational burden restricts the applicability of visual grounding to more intricate scenes, such as conversation-based reasoning segmentation, which involves lengthy language expressions. In this paper, we propose an efficient and effective multi-task visual grounding (EEVG) framework based on Transformer Decoder to address this issue, which reduces the cost in both language and visual aspects. In the language aspect, we employ the Transformer Decoder to fuse visual and linguistic features, where linguistic features are input as memory and visual features as queries. This allows fusion to scale linearly with language expression length. In the visual aspect, we introduce a parameter-free approach to reduce computation by eliminating background visual tokens based on attention scores. We then design a light mask head to directly predict segmentation masks from the remaining sparse feature maps. Extensive results and ablation studies on benchmarks demonstrate the efficiency and effectiveness of our approach. Code is available in https://github.com/chenwei746/EEVG.

Large Vision-Language Models (LVLMs) struggle with puzzles, which require precise perception, rule comprehension, and logical reasoning. Assessing and enhancing their performance in this domain is crucial, as it reflects their ability to engage in structured reasoning - an essential skill for real-world problem-solving. However, existing benchmarks primarily evaluate pre-trained models without additional training or fine-tuning, often lack a dedicated focus on reasoning, and fail to establish a systematic evaluation framework. To address these limitations, we introduce VGRP-Bench, a Visual Grid Reasoning Puzzle Benchmark featuring 20 diverse puzzles. VGRP-Bench spans multiple difficulty levels, and includes extensive experiments not only on existing chat LVLMs (e.g., GPT-4o), but also on reasoning LVLMs (e.g., Gemini-Thinking). Our results reveal that even the state-of-the-art LVLMs struggle with these puzzles, highlighting fundamental limitations in their puzzle-solving capabilities. Most importantly, through systematic experiments, we identify and analyze key factors influencing LVLMs' puzzle-solving performance, including the number of clues, grid size, and rule complexity. Furthermore, we explore two Supervised Fine-Tuning (SFT) strategies that can be used in post-training: SFT on solutions (S-SFT) and SFT on synthetic reasoning processes (R-SFT). While both methods significantly improve performance on trained puzzles, they exhibit limited generalization to unseen ones. We will release VGRP-Bench to facilitate further research on LVLMs for complex, real-world problem-solving. Project page: https://yufan-ren.com/subpage/VGRP-Bench/.

Current multimodal large language models (MLLMs) often underperform on mathematical problem-solving tasks that require fine-grained visual understanding. The limitation is largely attributable to inadequate perception of geometric primitives during image-level contrastive pre-training (e.g., CLIP). While recent efforts to improve math MLLMs have focused on scaling up mathematical visual instruction datasets and employing stronger LLM backbones, they often overlook persistent errors in visual recognition. In this paper, we systematically evaluate the visual grounding capabilities of state-of-the-art MLLMs and reveal a significant negative correlation between visual grounding accuracy and problem-solving performance, underscoring the critical role of fine-grained visual understanding. Notably, advanced models like GPT-4o exhibit a 70% error rate when identifying geometric entities, highlighting that this remains a key bottleneck in visual mathematical reasoning. To address this, we propose a novel approach, SVE-Math (Selective Vision-Enhanced Mathematical MLLM), featuring a geometric-grounded vision encoder and a feature router that dynamically adjusts the contribution of hierarchical visual feature maps. Our model recognizes accurate visual primitives and generates precise visual prompts tailored to the language model's reasoning needs. In experiments, SVE-Math-Qwen2.5-7B outperforms other 7B models by 15% on MathVerse and is compatible with GPT-4V on MathVista. Despite being trained on smaller datasets, SVE-Math-7B achieves competitive performance on GeoQA, rivaling models trained on significantly larger datasets. Our findings emphasize the importance of incorporating fine-grained visual understanding into MLLMs and provide a promising direction for future research.

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually is. We systematically assess which papers use which definitions and discuss how they relate to each other. We then analyze the computational complexity of counting the number of such regions for the various definitions. Generally, this turns out to be an intractable problem. We prove NP- and #P-hardness results already for networks with one hidden layer and strong hardness of approximation results for two or more hidden layers. Finally, on the algorithmic side, we demonstrate that counting linear regions can at least be achieved in polynomial space for some common definitions.

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

Visuals are valuable tools for teaching math word problems (MWPs), helping young learners interpret textual descriptions into mathematical expressions before solving them. However, creating such visuals is labor-intensive and there is a lack of automated methods to support this process. In this paper, we present Math2Visual, an automatic framework for generating pedagogically meaningful visuals from MWP text descriptions. Math2Visual leverages a pre-defined visual language and a design space grounded in interviews with math teachers, to illustrate the core mathematical relationships in MWPs. Using Math2Visual, we construct an annotated dataset of 1,903 visuals and evaluate Text-to-Image (TTI) models for their ability to generate visuals that align with our design. We further fine-tune several TTI models with our dataset, demonstrating improvements in educational visual generation. Our work establishes a new benchmark for automated generation of pedagogically meaningful visuals and offers insights into key challenges in producing multimodal educational content, such as the misrepresentation of mathematical relationships and the omission of essential visual elements.

Efficient and accurate feed-forward multi-view reconstruction has long been an important task in computer vision. Recent transformer-based models like VGGT and pi^3 have achieved impressive results with simple architectures, yet they face an inherent runtime bottleneck, due to the quadratic complexity of the global attention layers, that limits the scalability to large image sets. In this paper, we empirically analyze the global attention matrix of these models and observe that probability mass concentrates on a small subset of patch-patch interactions that correspond to cross-view geometric matches. Motivated by the structured attention and inspired by recent advancement in large language models, we propose a replacement for the dense global attention operation based on highly optimized block-sparse kernels, yielding up to 4times faster inference with comparable task performance. Our retrofit requires no retraining of the backbone, extends to both VGGT and pi^3, and supports large image collections. Evaluations on a comprehensive suite of multi-view benchmarks demonstrate the effectiveness of our approach.

Recent progress in multimodal reasoning has been driven largely by undisclosed datasets and proprietary data synthesis recipes, leaving open questions about how to systematically build large-scale, vision-centric reasoning datasets, particularly for tasks that go beyond visual math. In this work, we introduce a new reasoning data generation framework spanning diverse skills and levels of complexity with over 1M high-quality synthetic vision-centric questions. The dataset also includes preference data and instruction prompts supporting both offline and online RL. Our synthesis framework proceeds in two stages: (1) scale; and (2) complexity. Reasoning traces are then synthesized through a two-stage process that leverages VLMs and reasoning LLMs, producing CoT traces for VLMs that capture the richness and diverse cognitive behaviors found in frontier reasoning models. Remarkably, we show that finetuning Qwen2.5-VL-7B on our data outperforms all open-data baselines across all evaluated vision-centric benchmarks, and even surpasses strong closed-data models such as MiMo-VL-7B-RL on V* Bench, CV-Bench and MMStar-V. Perhaps most surprising, despite being entirely vision-centric, our data transfers positively to text-only reasoning (MMLU-Pro) and audio reasoning (MMAU), demonstrating its effectiveness. Similarly, despite not containing videos or embodied visual data, we observe notable gains when evaluating on a single-evidence embodied QA benchmark (NiEH). Finally, we use our data to analyze the entire VLM post-training pipeline. Our empirical analysis highlights that (i) SFT on high-quality data with non-linear reasoning traces is essential for effective online RL, (ii) staged offline RL matches online RL's performance while reducing compute demands, and (iii) careful SFT on high quality data can substantially improve out-of-domain, cross-modality transfer.

This paper reveals that many state-of-the-art large language models (LLMs) lack hierarchical knowledge about our visual world, unaware of even well-established biology taxonomies. This shortcoming makes LLMs a bottleneck for vision LLMs' hierarchical visual understanding (e.g., recognizing Anemone Fish but not Vertebrate). We arrive at these findings using about one million four-choice visual question answering (VQA) tasks constructed from six taxonomies and four image datasets. Interestingly, finetuning a vision LLM using our VQA tasks reaffirms LLMs' bottleneck effect to some extent because the VQA tasks improve the LLM's hierarchical consistency more than the vision LLM's. We conjecture that one cannot make vision LLMs understand visual concepts fully hierarchical until LLMs possess corresponding taxonomy knowledge.

Self-attention (SA) has become the cornerstone of modern vision backbones for its powerful expressivity over traditional Convolutions (Conv). However, its quadratic complexity remains a critical bottleneck for practical applications. Given that Conv offers linear complexity and strong visual priors, continuing efforts have been made to promote the renaissance of Conv. However, a persistent performance chasm remains, highlighting that these modernizations have not yet captured the intrinsic expressivity that defines SA. In this paper, we re-examine the design of the CNNs, directed by a key question: what principles give SA its edge over Conv? As a result, we reveal two fundamental insights that challenge the long-standing design intuitions in prior research (e.g., Receptive field). The two findings are: (1) Adaptive routing: SA dynamically regulates positional information flow according to semantic content, whereas Conv employs static kernels uniformly across all positions. (2) Lateral inhibition: SA induces score competition among token weighting, effectively suppressing redundancy and sharpening representations, whereas Conv filters lack such inhibitory dynamics and exhibit considerable redundancy. Based on this, we propose Attentive Convolution (ATConv), a principled reformulation of the convolutional operator that intrinsically injects these principles. Interestingly, with only 3times3 kernels, ATConv consistently outperforms various SA mechanisms in fundamental vision tasks. Building on ATConv, we introduce AttNet, a CNN family that can attain 84.4\% ImageNet-1K Top-1 accuracy with only 27M parameters. In diffusion-based image generation, replacing all SA with the proposed 3times 3 ATConv in SiT-XL/2 reduces ImageNet FID by 0.15 in 400k steps with faster sampling. Code is available at: github.com/price112/Attentive-Convolution.

The rapid advancements in Vision-Language Models (VLMs) have shown great potential in tackling mathematical reasoning tasks that involve visual context. Unlike humans who can reliably apply solution steps to similar problems with minor modifications, we found that SOTA VLMs like GPT-4o can consistently fail in these scenarios, revealing limitations in their mathematical reasoning capabilities. In this paper, we investigate the mathematical reasoning robustness in VLMs and evaluate how well these models perform under different variants of the same question, such as changes in visual numerical values or function graphs. While several vision-based math benchmarks have been developed to assess VLMs' problem-solving capabilities, these benchmarks contain only static sets of problems and cannot easily evaluate mathematical reasoning robustness. To fill this gap, we introduce DynaMath, a dynamic visual math benchmark designed for in-depth assessment of VLMs. DynaMath includes 501 high-quality, multi-topic seed questions, each represented as a Python program. Those programs are carefully designed and annotated to enable the automatic generation of a much larger set of concrete questions, including many different types of visual and textual variations. DynaMath allows us to evaluate the generalization ability of VLMs, by assessing their performance under varying input conditions of a seed question. We evaluated 14 SOTA VLMs with 5,010 generated concrete questions. Our results show that the worst-case model accuracy, defined as the percentage of correctly answered seed questions in all 10 variants, is significantly lower than the average-case accuracy. Our analysis emphasizes the need to study the robustness of VLMs' reasoning abilities, and DynaMath provides valuable insights to guide the development of more reliable models for mathematical reasoning.

Recent advances in vision transformers (ViTs) have demonstrated the advantage of global modeling capabilities, prompting widespread integration of large-kernel convolutions for enlarging the effective receptive field (ERF). However, the quadratic scaling of parameter count and computational complexity (FLOPs) with respect to kernel size poses significant efficiency and optimization challenges. This paper introduces RecConv, a recursive decomposition strategy that efficiently constructs multi-frequency representations using small-kernel convolutions. RecConv establishes a linear relationship between parameter growth and decomposing levels which determines the effective kernel size ktimes 2^ell for a base kernel k and ell levels of decomposition, while maintaining constant FLOPs regardless of the ERF expansion. Specifically, RecConv achieves a parameter expansion of only ell+2 times and a maximum FLOPs increase of 5/3 times, compared to the exponential growth (4^ell) of standard and depthwise convolutions. RecNeXt-M3 outperforms RepViT-M1.1 by 1.9 AP^{box} on COCO with similar FLOPs. This innovation provides a promising avenue towards designing efficient and compact networks across various modalities. Codes and models can be found at https://github.com/suous/RecNeXt.

Visual reasoning is critical for a wide range of computer vision tasks that go beyond surface-level object detection and classification. Despite notable advances in relational, symbolic, temporal, causal, and commonsense reasoning, existing surveys often address these directions in isolation, lacking a unified analysis and comparison across reasoning types, methodologies, and evaluation protocols. This survey aims to address this gap by categorizing visual reasoning into five major types (relational, symbolic, temporal, causal, and commonsense) and systematically examining their implementation through architectures such as graph-based models, memory networks, attention mechanisms, and neuro-symbolic systems. We review evaluation protocols designed to assess functional correctness, structural consistency, and causal validity, and critically analyze their limitations in terms of generalizability, reproducibility, and explanatory power. Beyond evaluation, we identify key open challenges in visual reasoning, including scalability to complex scenes, deeper integration of symbolic and neural paradigms, the lack of comprehensive benchmark datasets, and reasoning under weak supervision. Finally, we outline a forward-looking research agenda for next-generation vision systems, emphasizing that bridging perception and reasoning is essential for building transparent, trustworthy, and cross-domain adaptive AI systems, particularly in critical domains such as autonomous driving and medical diagnostics.

The quadratic complexity of full attention mechanisms poses a significant bottleneck for Video Diffusion Models (VDMs) aiming to generate long-duration, high-resolution videos. While various sparse attention methods have been proposed, many are designed as training-free inference accelerators or do not optimally capture the unique spatio-temporal characteristics inherent in video data when trained natively. This paper introduces Video Mixture of Block Attention (VMoBA), a novel sparse attention mechanism specifically adapted for VDMs. Motivated by an in-depth analysis of attention patterns within pre-trained video transformers, which revealed strong spatio-temporal locality, varying query importance, and head-specific concentration levels, VMoBA enhances the original MoBA framework with three key modifications: (1) a layer-wise recurrent block partition scheme (1D-2D-3D) to dynamically adapt to diverse spatio-temporal attention patterns and improve efficiency; (2) global block selection to prioritize the most salient query-key block interactions across an entire attention head; and (3) threshold-based block selection to dynamically determine the number of attended blocks based on their cumulative similarity. Extensive experiments demonstrate that VMoBA significantly accelerates the training of VDMs on longer sequences, achieving 2.92x FLOPs and 1.48x latency speedup, while attaining comparable or even superior generation quality to full attention. Furthermore, VMoBA exhibits competitive performance in training-free inference, offering 2.40x FLOPs and 1.35x latency speedup for high-res video generation.

The transformer architecture has driven breakthroughs in recent years on tasks which require modeling pairwise relationships between sequential elements, as is the case in natural language understanding. However, long seqeuences pose a problem due to the quadratic complexity of the attention operation. Previous research has aimed to lower the complexity by sparsifying or linearly approximating the attention matrix. Yet, these approaches cannot straightforwardly distill knowledge from a teacher's attention matrix and often require complete retraining from scratch. Furthermore, previous sparse and linear approaches lose interpretability if they cannot produce full attention matrices. To address these challenges, we propose SEA: Sparse linear attention with an Estimated Attention mask. SEA estimates the attention matrix with linear complexity via kernel-based linear attention, then subsequently creates a sparse attention matrix with a top-k selection to perform a sparse attention operation. For language modeling tasks (Wikitext2), previous linear and sparse attention methods show roughly two-fold worse perplexity scores over the quadratic OPT-1.3B baseline, while SEA achieves better perplexity than OPT-1.3B, using roughly half the memory of OPT-1.3B, providing interpretable attention matrix. We believe that our work will have a large practical impact, as it opens the possibility of running large transformers on resource-limited devices with less memory.

Recent advances in deep generative models have lead to remarkable progress in synthesizing high quality images. Following their successful application in image processing and representation learning, an important next step is to consider videos. Learning generative models of video is a much harder task, requiring a model to capture the temporal dynamics of a scene, in addition to the visual presentation of objects. While recent attempts at formulating generative models of video have had some success, current progress is hampered by (1) the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples, and (2) the wide gap between purely synthetic video data sets and challenging real-world data sets in terms of complexity. To this extent we propose Fr\'{e}chet Video Distance (FVD), a new metric for generative models of video, and StarCraft 2 Videos (SCV), a benchmark of game play from custom starcraft 2 scenarios that challenge the current capabilities of generative models of video. We contribute a large-scale human study, which confirms that FVD correlates well with qualitative human judgment of generated videos, and provide initial benchmark results on SCV.

The attention module, which is a crucial component in Transformer, cannot scale efficiently to long sequences due to its quadratic complexity. Many works focus on approximating the dot-then-exponentiate softmax function in the original attention, leading to sub-quadratic or even linear-complexity Transformer architectures. However, we show that these methods cannot be applied to more powerful attention modules that go beyond the dot-then-exponentiate style, e.g., Transformers with relative positional encoding (RPE). Since in many state-of-the-art models, relative positional encoding is used as default, designing efficient Transformers that can incorporate RPE is appealing. In this paper, we propose a novel way to accelerate attention calculation for Transformers with RPE on top of the kernelized attention. Based upon the observation that relative positional encoding forms a Toeplitz matrix, we mathematically show that kernelized attention with RPE can be calculated efficiently using Fast Fourier Transform (FFT). With FFT, our method achieves O(nlog n) time complexity. Interestingly, we further demonstrate that properly using relative positional encoding can mitigate the training instability problem of vanilla kernelized attention. On a wide range of tasks, we empirically show that our models can be trained from scratch without any optimization issues. The learned model performs better than many efficient Transformer variants and is faster than standard Transformer in the long-sequence regime.

While Large Language Models (LLMs) have excelled in textual reasoning, they struggle with mathematical domains like geometry that intrinsically rely on visual aids. Existing approaches to Visual Chain-of-Thought (VCoT) are often limited by rigid external tools or fail to generate the high-fidelity, strategically-timed diagrams necessary for complex problem-solving. To bridge this gap, we introduce MathCanvas, a comprehensive framework designed to endow unified Large Multimodal Models (LMMs) with intrinsic VCoT capabilities for mathematics. Our approach consists of two phases. First, a Visual Manipulation stage pre-trains the model on a novel 15.2M-pair corpus, comprising 10M caption-to-diagram pairs (MathCanvas-Imagen) and 5.2M step-by-step editing trajectories (MathCanvas-Edit), to master diagram generation and editing. Second, a Strategic Visual-Aided Reasoning stage fine-tunes the model on MathCanvas-Instruct, a new 219K-example dataset of interleaved visual-textual reasoning paths, teaching it when and how to leverage visual aids. To facilitate rigorous evaluation, we introduce MathCanvas-Bench, a challenging benchmark with 3K problems that require models to produce interleaved visual-textual solutions. Our model, BAGEL-Canvas, trained under this framework, achieves an 86% relative improvement over strong LMM baselines on MathCanvas-Bench, demonstrating excellent generalization to other public math benchmarks. Our work provides a complete toolkit-framework, datasets, and benchmark-to unlock complex, human-like visual-aided reasoning in LMMs. Project Page: https://mathcanvas.github.io/

Large Multimodal Models (LMMs) have recently demonstrated remarkable visual understanding performance on both vision-language and vision-centric tasks. However, they often fall short in integrating advanced, task-specific capabilities for compositional reasoning, which hinders their progress toward truly competent general vision models. To address this, we present a unified visual reasoning mechanism that enables LMMs to solve complicated compositional problems by leveraging their intrinsic capabilities (e.g. grounding and visual understanding capabilities). Different from the previous shortcut learning mechanism, our approach introduces a human-like understanding-thinking-answering process, allowing the model to complete all steps in a single pass forwarding without the need for multiple inferences or external tools. This design bridges the gap between foundational visual capabilities and general question answering, encouraging LMMs to generate faithful and traceable responses for complex visual reasoning. Meanwhile, we curate 334K visual instruction samples covering both general scenes and text-rich scenes and involving multiple foundational visual capabilities. Our trained model, Griffon-R, has the ability of end-to-end automatic understanding, self-thinking, and reasoning answers. Comprehensive experiments show that Griffon-R not only achieves advancing performance on complex visual reasoning benchmarks including VSR and CLEVR, but also enhances multimodal capabilities across various benchmarks like MMBench and ScienceQA. Data, models, and codes will be release at https://github.com/jefferyZhan/Griffon/tree/master/Griffon-R soon.

Complex visual reasoning remains a key challenge today. Typically, the challenge is tackled using methodologies such as Chain of Thought (COT) and visual instruction tuning. However, how to organically combine these two methodologies for greater success remains unexplored. Also, issues like hallucinations and high training cost still need to be addressed. In this work, we devise an innovative multi-round training and reasoning framework suitable for lightweight Multimodal Large Language Models (MLLMs). Our self-questioning approach heuristically guides MLLMs to focus on visual clues relevant to the target problem, reducing hallucinations and enhancing the model's ability to describe fine-grained image details. This ultimately enables the model to perform well in complex visual reasoning and question-answering tasks. We have named this framework Socratic Questioning(SQ). To facilitate future research, we create a multimodal mini-dataset named CapQA, which includes 1k images of fine-grained activities, for visual instruction tuning and evaluation, our proposed SQ method leads to a 31.2% improvement in the hallucination score. Our extensive experiments on various benchmarks demonstrate SQ's remarkable capabilities in heuristic self-questioning, zero-shot visual reasoning and hallucination mitigation. Our model and code will be publicly available.

Recent advances in Vision-Language Models (VLMs) and large language models (LLMs) have greatly enhanced visual reasoning, a key capability for embodied AI agents like robots. However, existing visual reasoning benchmarks often suffer from several limitations: they lack a clear definition of reasoning complexity, offer have no control to generate questions over varying difficulty and task customization, and fail to provide structured, step-by-step reasoning annotations (workflows). To bridge these gaps, we formalize reasoning complexity, introduce an adaptive query engine that generates customizable questions of varying complexity with detailed intermediate annotations, and extend the JRDB dataset with human-object interaction and geometric relationship annotations to create JRDB-Reasoning, a benchmark tailored for visual reasoning in human-crowded environments. Our engine and benchmark enable fine-grained evaluation of visual reasoning frameworks and dynamic assessment of visual-language models across reasoning levels.

Diffusion Transformers (DiT) have become a leading architecture in image generation. However, the quadratic complexity of attention mechanisms, which are responsible for modeling token-wise relationships, results in significant latency when generating high-resolution images. To address this issue, we aim at a linear attention mechanism in this paper that reduces the complexity of pre-trained DiTs to linear. We begin our exploration with a comprehensive summary of existing efficient attention mechanisms and identify four key factors crucial for successful linearization of pre-trained DiTs: locality, formulation consistency, high-rank attention maps, and feature integrity. Based on these insights, we introduce a convolution-like local attention strategy termed CLEAR, which limits feature interactions to a local window around each query token, and thus achieves linear complexity. Our experiments indicate that, by fine-tuning the attention layer on merely 10K self-generated samples for 10K iterations, we can effectively transfer knowledge from a pre-trained DiT to a student model with linear complexity, yielding results comparable to the teacher model. Simultaneously, it reduces attention computations by 99.5% and accelerates generation by 6.3 times for generating 8K-resolution images. Furthermore, we investigate favorable properties in the distilled attention layers, such as zero-shot generalization cross various models and plugins, and improved support for multi-GPU parallel inference. Models and codes are available here: https://github.com/Huage001/CLEAR.

We present a simple method that achieves unexpectedly superior performance for Complex Reasoning involved Visual Question Answering. Our solution collects statistical features from high-frequency words of all the questions asked about an image and use them as accurate knowledge for answering further questions of the same image. We are fully aware that this setting is not ubiquitously applicable, and in a more common setting one should assume the questions are asked separately and they cannot be gathered to obtain a knowledge base. Nonetheless, we use this method as an evidence to demonstrate our observation that the bottleneck effect is more severe on the feature extraction part than it is on the knowledge reasoning part. We show significant gaps when using the same reasoning model with 1) ground-truth features; 2) statistical features; 3) detected features from completely learned detectors, and analyze what these gaps mean to researches on visual reasoning topics. Our model with the statistical features achieves the 2nd place in the GQA Challenge 2019.

Large language models (LLMs) have demonstrated significant capabilities in mathematical reasoning, particularly with text-based mathematical problems. However, current multi-modal large language models (MLLMs), especially those specialized in mathematics, tend to focus predominantly on solving geometric problems but ignore the diversity of visual information available in other areas of mathematics. Moreover, the geometric information for these specialized mathematical MLLMs is derived from several public datasets, which are typically limited in diversity and complexity. To address these limitations, we aim to construct a fine-tuning dataset named MathVL, and develop a series of specialized mathematical MLLMs termed MathGLM-Vision by conducting Supervised Fine-Tuning (SFT) on MathVL with various parameter-scale backbones. To extensively evaluate the effectiveness of MathGLM-Vision, we conduct experiments on several public benchmarks and our curated MathVL-test consisting of 2,000 problems. Experimental results demonstrate that MathGLM-Vision achieves significant improvements compared with some existing models, including backbone models and open-source mathematical MLLMs. These findings indicate the importance of diversity dataset in enhancing the mathematical reasoning abilities of MLLMs.

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

Despite the recent success in many applications, the high computational requirements of vision transformers limit their use in resource-constrained settings. While many existing methods improve the quadratic complexity of attention, in most vision transformers, self-attention is not the major computation bottleneck, e.g., more than 80% of the computation is spent on fully-connected layers. To improve the computational complexity of all layers, we propose a novel token downsampling method, called Token Pooling, efficiently exploiting redundancies in the images and intermediate token representations. We show that, under mild assumptions, softmax-attention acts as a high-dimensional low-pass (smoothing) filter. Thus, its output contains redundancy that can be pruned to achieve a better trade-off between the computational cost and accuracy. Our new technique accurately approximates a set of tokens by minimizing the reconstruction error caused by downsampling. We solve this optimization problem via cost-efficient clustering. We rigorously analyze and compare to prior downsampling methods. Our experiments show that Token Pooling significantly improves the cost-accuracy trade-off over the state-of-the-art downsampling. Token Pooling is a simple and effective operator that can benefit many architectures. Applied to DeiT, it achieves the same ImageNet top-1 accuracy using 42% fewer computations.

The releases of OpenAI's o1 and o3 mark a significant paradigm shift in Large Language Models towards advanced reasoning capabilities. Notably, o3 outperformed humans in novel problem-solving and skill acquisition on the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI). However, this benchmark is limited to symbolic patterns, whereas humans often perceive and reason about multimodal scenarios involving both vision and language data. Thus, there is an urgent need to investigate advanced reasoning capabilities in multimodal tasks. To this end, we track the evolution of the GPT-[n] and o-[n] series models on challenging multimodal puzzles, requiring fine-grained visual perception with abstract or algorithmic reasoning. The superior performance of o1 comes at nearly 750 times the computational cost of GPT-4o, raising concerns about its efficiency. Our results reveal a clear upward trend in reasoning capabilities across model iterations, with notable performance jumps across GPT-series models and subsequently to o1. Nonetheless, we observe that the o1 model still struggles with simple multimodal puzzles requiring abstract reasoning. Furthermore, its performance in algorithmic puzzles remains poor. We plan to continuously track new models in the series and update our results in this paper accordingly. All resources used in this evaluation are openly available https://github.com/declare-lab/LLM-PuzzleTest.

Measuring the perception of visual content is a long-standing problem in computer vision. Many mathematical models have been developed to evaluate the look or quality of an image. Despite the effectiveness of such tools in quantifying degradations such as noise and blurriness levels, such quantification is loosely coupled with human language. When it comes to more abstract perception about the feel of visual content, existing methods can only rely on supervised models that are explicitly trained with labeled data collected via laborious user study. In this paper, we go beyond the conventional paradigms by exploring the rich visual language prior encapsulated in Contrastive Language-Image Pre-training (CLIP) models for assessing both the quality perception (look) and abstract perception (feel) of images in a zero-shot manner. In particular, we discuss effective prompt designs and show an effective prompt pairing strategy to harness the prior. We also provide extensive experiments on controlled datasets and Image Quality Assessment (IQA) benchmarks. Our results show that CLIP captures meaningful priors that generalize well to different perceptual assessments. Code is avaliable at https://github.com/IceClear/CLIP-IQA.

We explore multi-step reasoning in vision-language models (VLMs). The problem is challenging, as reasoning data consisting of multiple steps of visual and language processing are barely available. To overcome the challenge, we first introduce a least-to-most visual reasoning paradigm, which interleaves steps of decomposing a question into sub-questions and invoking external tools for resolving sub-questions. Based on the paradigm, we further propose a novel data synthesis approach that can automatically create questions and multi-step reasoning paths for an image in a bottom-up manner. Our approach divides the complex synthesis task into a few simple sub-tasks, and (almost entirely) relies on open-sourced models to accomplish the sub-tasks. Therefore, the entire synthesis process is reproducible and cost-efficient, and the synthesized data is quality guaranteed. With the approach, we construct 50k visual reasoning examples. Then, we develop a visual reasoner through supervised fine-tuning, which is capable of generally enhancing the reasoning abilities of a wide range of existing VLMs in a plug-and-play fashion. Extensive experiments indicate that the visual reasoner can consistently and significantly improve four VLMs on four VQA benchmarks. Our code and dataset are available at https://github.com/steven-ccq/VisualReasoner.

Evaluating the robustness of Large Vision-Language Models (LVLMs) is essential for their continued development and responsible deployment in real-world applications. However, existing robustness benchmarks typically focus on hallucination or misleading textual inputs, while largely overlooking the equally critical challenge posed by misleading visual inputs in assessing visual understanding. To fill this important gap, we introduce MVI-Bench, the first comprehensive benchmark specially designed for evaluating how Misleading Visual Inputs undermine the robustness of LVLMs. Grounded in fundamental visual primitives, the design of MVI-Bench centers on three hierarchical levels of misleading visual inputs: Visual Concept, Visual Attribute, and Visual Relationship. Using this taxonomy, we curate six representative categories and compile 1,248 expertly annotated VQA instances. To facilitate fine-grained robustness evaluation, we further introduce MVI-Sensitivity, a novel metric that characterizes LVLM robustness at a granular level. Empirical results across 18 state-of-the-art LVLMs uncover pronounced vulnerabilities to misleading visual inputs, and our in-depth analyses on MVI-Bench provide actionable insights that can guide the development of more reliable and robust LVLMs. The benchmark and codebase can be accessed at https://github.com/chenyil6/MVI-Bench.

Visual prompt engineering is a fundamental technology in the field of visual and image Artificial General Intelligence, serving as a key component for achieving zero-shot capabilities. As the development of large vision models progresses, the importance of prompt engineering becomes increasingly evident. Designing suitable prompts for specific visual tasks has emerged as a meaningful research direction. This review aims to summarize the methods employed in the computer vision domain for large vision models and visual prompt engineering, exploring the latest advancements in visual prompt engineering. We present influential large models in the visual domain and a range of prompt engineering methods employed on these models. It is our hope that this review provides a comprehensive and systematic description of prompt engineering methods based on large visual models, offering valuable insights for future researchers in their exploration of this field.

In computer vision, a larger effective receptive field (ERF) is associated with better performance. While attention natively supports global context, its quadratic complexity limits its applicability to tasks that benefit from high-resolution input. In this work, we extend Hyena, a convolution-based attention replacement, from causal sequences to bidirectional data and two-dimensional image space. We scale Hyena's convolution kernels beyond the feature map size, up to 191times191, to maximize ERF while maintaining sub-quadratic complexity in the number of pixels. We integrate our two-dimensional Hyena, HyenaPixel, and bidirectional Hyena into the MetaFormer framework. For image categorization, HyenaPixel and bidirectional Hyena achieve a competitive ImageNet-1k top-1 accuracy of 84.9% and 85.2%, respectively, with no additional training data, while outperforming other convolutional and large-kernel networks. Combining HyenaPixel with attention further improves accuracy. We attribute the success of bidirectional Hyena to learning the data-dependent geometric arrangement of pixels without a fixed neighborhood definition. Experimental results on downstream tasks suggest that HyenaPixel with large filters and a fixed neighborhood leads to better localization performance.

The quadratic time and memory complexity of the attention mechanism in modern Transformer based video generators makes end-to-end training for ultra high resolution videos prohibitively expensive. Motivated by this limitation, we introduce a training-free approach that leverages video Diffusion Transformers pretrained at their native scale to synthesize higher resolution videos without any additional training or adaptation. At the core of our method lies an inward sliding window attention mechanism, which originates from a key observation: maintaining each query token's training scale receptive field is crucial for preserving visual fidelity and detail. However, naive local window attention, unfortunately, often leads to repetitive content and exhibits a lack of global coherence in the generated results. To overcome this challenge, we devise a dual-path pipeline that backs up window attention with a novel cross-attention override strategy, enabling the semantic content produced by local attention to be guided by another branch with a full receptive field and, therefore, ensuring holistic consistency. Furthermore, to improve efficiency, we incorporate a cross-attention caching strategy for this branch to avoid the frequent computation of full 3D attention. Extensive experiments demonstrate that our method delivers ultra-high-resolution videos with fine-grained visual details and high efficiency in a training-free paradigm. Meanwhile, it achieves superior performance on VBench, even compared to training-based alternatives, with competitive or improved efficiency. Codes are available at: https://github.com/WillWu111/FreeSwim

We study the representation complexity of model-based and model-free reinforcement learning (RL) in the context of circuit complexity. We prove theoretically that there exists a broad class of MDPs such that their underlying transition and reward functions can be represented by constant depth circuits with polynomial size, while the optimal Q-function suffers an exponential circuit complexity in constant-depth circuits. By drawing attention to the approximation errors and building connections to complexity theory, our theory provides unique insights into why model-based algorithms usually enjoy better sample complexity than model-free algorithms from a novel representation complexity perspective: in some cases, the ground-truth rule (model) of the environment is simple to represent, while other quantities, such as Q-function, appear complex. We empirically corroborate our theory by comparing the approximation error of the transition kernel, reward function, and optimal Q-function in various Mujoco environments, which demonstrates that the approximation errors of the transition kernel and reward function are consistently lower than those of the optimal Q-function. To the best of our knowledge, this work is the first to study the circuit complexity of RL, which also provides a rigorous framework for future research.

Vision transformers have demonstrated remarkable success in a wide range of computer vision tasks over the last years. However, their high computational costs remain a significant barrier to their practical deployment. In particular, the complexity of transformer models is quadratic with respect to the number of input tokens. Therefore techniques that reduce the number of input tokens that need to be processed have been proposed. This paper introduces Learned Thresholds token Merging and Pruning (LTMP), a novel approach that leverages the strengths of both token merging and token pruning. LTMP uses learned threshold masking modules that dynamically determine which tokens to merge and which to prune. We demonstrate our approach with extensive experiments on vision transformers on the ImageNet classification task. Our results demonstrate that LTMP achieves state-of-the-art accuracy across reduction rates while requiring only a single fine-tuning epoch, which is an order of magnitude faster than previous methods. Code is available at https://github.com/Mxbonn/ltmp .

Despite the successes of recent developments in visual AI, different shortcomings still exist; from missing exact logical reasoning, to abstract generalization abilities, to understanding complex and noisy scenes. Unfortunately, existing benchmarks, were not designed to capture more than a few of these aspects. Whereas deep learning datasets focus on visually complex data but simple visual reasoning tasks, inductive logic datasets involve complex logical learning tasks, however, lack the visual component. To address this, we propose the visual logical learning dataset, V-LoL, that seamlessly combines visual and logical challenges. Notably, we introduce the first instantiation of V-LoL, V-LoL-Trains, -- a visual rendition of a classic benchmark in symbolic AI, the Michalski train problem. By incorporating intricate visual scenes and flexible logical reasoning tasks within a versatile framework, V-LoL-Trains provides a platform for investigating a wide range of visual logical learning challenges. We evaluate a variety of AI systems including traditional symbolic AI, neural AI, as well as neuro-symbolic AI. Our evaluations demonstrate that even state-of-the-art AI faces difficulties in dealing with visual logical learning challenges, highlighting unique advantages and limitations specific to each methodology. Overall, V-LoL opens up new avenues for understanding and enhancing current abilities in visual logical learning for AI systems.

Current benchmarks for evaluating Vision Language Models (VLMs) often fall short in thoroughly assessing model abilities to understand and process complex visual and textual content. They typically focus on simple tasks that do not require deep reasoning or the integration of multiple data modalities to solve an original problem. To address this gap, we introduce the PARROT-360V Benchmark, a novel and comprehensive benchmark featuring 2487 challenging visual puzzles designed to test VLMs on complex visual reasoning tasks. We evaluated leading models: GPT-4o, Claude-3.5-Sonnet, and Gemini-1.5-Pro, using PARROT-360V to assess their capabilities in combining visual clues with language skills to solve tasks in a manner akin to human problem-solving. Our findings reveal a notable performance gap: state-of-the-art models scored between 28 to 56 percentage on our benchmark, significantly lower than their performance on popular benchmarks. This underscores the limitations of current VLMs in handling complex, multi-step reasoning tasks and highlights the need for more robust evaluation frameworks to advance the field.

Large Multimodal Models (LMMs) have achieved remarkable progress across various capabilities; however, complex video reasoning in the scientific domain remains a significant and challenging frontier. Current video benchmarks predominantly target general scenarios where perception/recognition is heavily relied on, while with relatively simple reasoning tasks, leading to saturation and thus failing to effectively evaluate advanced multimodal cognitive skills. To address this critical gap, we introduce SciVideoBench, a rigorous benchmark specifically designed to assess advanced video reasoning in scientific contexts. SciVideoBench consists of 1,000 carefully crafted multiple-choice questions derived from cutting-edge scientific experimental videos spanning over 25 specialized academic subjects and verified by a semi-automatic system. Each question demands sophisticated domain-specific knowledge, precise spatiotemporal perception, and intricate logical reasoning, effectively challenging models' higher-order cognitive abilities. Our evaluation highlights significant performance deficits in state-of-the-art proprietary and open-source LMMs, including Gemini 2.5 Pro and Qwen2.5-VL, indicating substantial room for advancement in video reasoning capabilities. Detailed analyses of critical factors such as reasoning complexity and visual grounding provide valuable insights and clear direction for future developments in LMMs, driving the evolution of truly capable multimodal AI co-scientists. We hope SciVideoBench could fit the interests of the community and help to push the boundary of cutting-edge AI for border science.

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

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Text-to-video generation enhances content creation but is highly computationally intensive: The computational cost of Diffusion Transformers (DiTs) scales quadratically in the number of pixels. This makes minute-length video generation extremely expensive, limiting most existing models to generating videos of only 10-20 seconds length. We propose a Linear-complexity text-to-video Generation (LinGen) framework whose cost scales linearly in the number of pixels. For the first time, LinGen enables high-resolution minute-length video generation on a single GPU without compromising quality. It replaces the computationally-dominant and quadratic-complexity block, self-attention, with a linear-complexity block called MATE, which consists of an MA-branch and a TE-branch. The MA-branch targets short-to-long-range correlations, combining a bidirectional Mamba2 block with our token rearrangement method, Rotary Major Scan, and our review tokens developed for long video generation. The TE-branch is a novel TEmporal Swin Attention block that focuses on temporal correlations between adjacent tokens and medium-range tokens. The MATE block addresses the adjacency preservation issue of Mamba and improves the consistency of generated videos significantly. Experimental results show that LinGen outperforms DiT (with a 75.6% win rate) in video quality with up to 15times (11.5times) FLOPs (latency) reduction. Furthermore, both automatic metrics and human evaluation demonstrate our LinGen-4B yields comparable video quality to state-of-the-art models (with a 50.5%, 52.1%, 49.1% win rate with respect to Gen-3, LumaLabs, and Kling, respectively). This paves the way to hour-length movie generation and real-time interactive video generation. We provide 68s video generation results and more examples in our project website: https://lineargen.github.io/.

This paper delves into the interplay between vision backbones and optimizers, unvealing an inter-dependent phenomenon termed \textbf{backbone-optimizer coupling bias} (BOCB). We observe that canonical CNNs, such as VGG and ResNet, exhibit a marked co-dependency with SGD families, while recent architectures like ViTs and ConvNeXt share a tight coupling with the adaptive learning rate ones. We further show that BOCB can be introduced by both optimizers and certain backbone designs and may significantly impact the pre-training and downstream fine-tuning of vision models. Through in-depth empirical analysis, we summarize takeaways on recommended optimizers and insights into robust vision backbone architectures. We hope this work can inspire the community to question long-held assumptions on backbones and optimizers, stimulate further explorations, and thereby contribute to more robust vision systems. The source code and models are publicly available at https://bocb-ai.github.io/.

Despite rapid advances in vision-language models (VLMs), current benchmarks for multimodal reasoning fall short in three key dimensions. First, they overwhelmingly rely on static images, failing to capture the temporal complexity of real-world environments. Second, they narrowly focus on mathematical problem-solving, neglecting the broader spectrum of reasoning skills -- including abstract, physical, planning, spatial, and temporal capabilities -- required for robust multimodal intelligence. Third, many benchmarks quickly saturate, offering limited headroom for diagnosing failure modes or measuring continued progress. We introduce MORSE-500 (Multimodal Reasoning Stress-test Environment), a video benchmark composed of 500 fully scripted clips with embedded questions spanning six complementary reasoning categories. Each instance is programmatically generated using deterministic Python scripts (via Manim, Matplotlib, MoviePy), generative video models, and curated real footage. This script-driven design allows fine-grained control over visual complexity, distractor density, and temporal dynamics -- enabling difficulty to be scaled systematically as models improve. Unlike static benchmarks that become obsolete once saturated, MORSE-500 is built to evolve: its controllable generation pipeline supports the creation of arbitrarily challenging new instances, making it ideally suited for stress-testing next-generation models. Initial experiments with state-of-the-art systems -- including various Gemini 2.5 Pro and OpenAI o3 which represent the strongest available at the time, alongside strong open-source models -- reveal substantial performance gaps across all categories, with particularly large deficits in abstract and planning tasks. We release the full dataset, generation scripts, and evaluation harness to support transparent, reproducible, and forward-looking multimodal reasoning research.

We present v1, a lightweight extension to Multimodal Large Language Models (MLLMs) that enables selective visual revisitation during inference. While current MLLMs typically consume visual input only once and reason purely over internal memory, v1 introduces a simple point-and-copy mechanism that allows the model to dynamically retrieve relevant image regions throughout the reasoning process. This mechanism augments existing architectures with minimal modifications, enabling contextual access to visual tokens based on the model's evolving hypotheses. To train this capability, we construct v1g, a dataset of 300K multimodal reasoning traces with interleaved visual grounding annotations. Experiments on three multimodal mathematical reasoning benchmarks -- MathVista, MathVision, and MathVerse -- demonstrate that v1 consistently improves performance over comparable baselines, particularly on tasks requiring fine-grained visual reference and multi-step reasoning. Our results suggest that dynamic visual access is a promising direction for enhancing grounded multimodal reasoning. Code, models, and data will be released to support future research.

Vision language models (VLMs) have achieved impressive performance across a variety of computer vision tasks. However, the multimodal reasoning capability has not been fully explored in existing models. In this paper, we propose a Chain-of-Focus (CoF) method that allows VLMs to perform adaptive focusing and zooming in on key image regions based on obtained visual cues and the given questions, achieving efficient multimodal reasoning. To enable this CoF capability, we present a two-stage training pipeline, including supervised fine-tuning (SFT) and reinforcement learning (RL). In the SFT stage, we construct the MM-CoF dataset, comprising 3K samples derived from a visual agent designed to adaptively identify key regions to solve visual tasks with different image resolutions and questions. We use MM-CoF to fine-tune the Qwen2.5-VL model for cold start. In the RL stage, we leverage the outcome accuracies and formats as rewards to update the Qwen2.5-VL model, enabling further refining the search and reasoning strategy of models without human priors. Our model achieves significant improvements on multiple benchmarks. On the V* benchmark that requires strong visual reasoning capability, our model outperforms existing VLMs by 5% among 8 image resolutions ranging from 224 to 4K, demonstrating the effectiveness of the proposed CoF method and facilitating the more efficient deployment of VLMs in practical applications.

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

Reinforcement learning (RL) has shown great effectiveness for fine-tuning large language models (LLMs) using tasks that are challenging yet easily verifiable, such as math reasoning or code generation. However, extending this success to visual perception in vision-language models (VLMs) has been impeded by the scarcity of vision-centric tasks that are simultaneously challenging and unambiguously verifiable. To this end, we introduce ViCrit (Visual Caption Hallucination Critic), an RL proxy task that trains VLMs to localize a subtle, synthetic visual hallucination injected into paragraphs of human-written image captions. Starting from a 200-word captions, we inject a single, subtle visual description error-altering a few words on objects, attributes, counts, or spatial relations-and task the model to pinpoint the corrupted span given the image and the modified caption. This formulation preserves the full perceptual difficulty while providing a binary, exact-match reward that is easy to compute and unambiguous. Models trained with the ViCrit Task exhibit substantial gains across a variety of VL benchmarks. Crucially, the improvements transfer beyond natural-image training data to abstract image reasoning and visual math, showing promises of learning to perceive rather than barely memorizing seen objects. To facilitate evaluation, we further introduce ViCrit-Bench, a category-balanced diagnostic benchmark that systematically probes perception errors across diverse image domains and error types. Together, our results demonstrate that fine-grained hallucination criticism is an effective and generalizable objective for enhancing visual perception in VLMs.

Multi-modal Chain-of-Thought (MCoT) requires models to leverage knowledge from both textual and visual modalities for step-by-step reasoning, which gains increasing attention. Nevertheless, the current MCoT benchmark still faces some challenges: (1) absence of visual modal reasoning, (2) single-step visual modal reasoning, and (3) Domain missing, thereby hindering the development of MCoT. Motivated by this, we introduce a novel benchmark (M^3CoT) to address the above challenges, advancing the multi-domain, multi-step, and multi-modal CoT. Additionally, we conduct a thorough evaluation involving abundant MCoT approaches on Vision Large Language Models (VLLMs). In addition, we highlight that the current VLLMs still struggle to correctly reason in M^3CoT and there remains a large gap between existing VLLMs and human performance in M^3CoT, despite their superior results on previous MCoT benchmarks. To our knowledge, we take the first meaningful step toward the multi-domain, multi-step, and multi-modal scenario in MCoT. We hope that M^3CoT can serve as a valuable resource, providing a pioneering foundation in multi-domain, multi-step, multi-modal chain-of-thought research.

Efficient processing of high-resolution images is crucial for real-world vision-language applications. However, existing Large Vision-Language Models (LVLMs) incur substantial computational overhead due to the large number of vision tokens. With the advent of "thinking with images" models, reasoning now extends beyond text to the visual domain. This capability motivates our two-stage "coarse-to-fine" reasoning pipeline: first, a downsampled image is analyzed to identify task-relevant regions; then, only these regions are cropped at full resolution and processed in a subsequent reasoning stage. This approach reduces computational cost while preserving fine-grained visual details where necessary. A major challenge lies in inferring which regions are truly relevant to a given query. Recent related methods often fail in the first stage after input-image downsampling, due to perception-driven reasoning, where clear visual information is required for effective reasoning. To address this issue, we propose ERGO (Efficient Reasoning & Guided Observation) that performs reasoning-driven perception-leveraging multimodal context to determine where to focus. Our model can account for perceptual uncertainty, expanding the cropped region to cover visually ambiguous areas for answering questions. To this end, we develop simple yet effective reward components in a reinforcement learning framework for coarse-to-fine perception. Across multiple datasets, our approach delivers higher accuracy than the original model and competitive methods, with greater efficiency. For instance, ERGO surpasses Qwen2.5-VL-7B on the V* benchmark by 4.7 points while using only 23% of the vision tokens, achieving a 3x inference speedup. The code and models can be found at: https://github.com/nota-github/ERGO.

Multimodal Large Language Models (MLLMs) show reasoning promise, yet their visual perception is a critical bottleneck. Strikingly, MLLMs can produce correct answers even while misinterpreting crucial visual elements, masking these underlying failures. Our preliminary study on a joint perception-reasoning dataset revealed that for one leading MLLM, 29% of its correct answers to reasoning questions still exhibited visual perception errors. To systematically address this, we introduce "Do You See Me", a scalable benchmark with 1,758 images and 2,612 questions. It spans seven human-psychology inspired subtasks in 2D and 3D, featuring controllable complexity to rigorously evaluate MLLM visual skills. Our findings on 3 leading closed-source and 5 major open-source models reveal a stark deficit: humans achieve 96.49% accuracy, while top MLLMs average below 50%. This performance gap widens rapidly with increased task complexity (e.g., from 12% to 45% in the visual form constancy subtask). Further analysis into the root causes suggests that failures stem from challenges like misallocated visual attention and the instability of internal representations for fine-grained details, especially at or below encoder patch resolution. This underscores an urgent need for MLLMs with truly robust visual perception. The benchmark dataset, source code and evaluation scripts are available at https://github.com/microsoft/Do-You-See-Me.

The attention mechanism of a transformer has a quadratic complexity, leading to high inference costs and latency for long sequences. However, attention matrices are mostly sparse, which implies that many entries may be omitted from computation for efficient inference. Sparse attention inference methods aim to reduce this computational burden; however, they also come with a troublesome performance degradation. We discover that one reason for this degradation is that the sparse calculation induces a distributional shift in the attention outputs. The distributional shift causes decoding-time queries to fail to align well with the appropriate keys from the prefill stage, leading to a drop in performance. We propose a simple, novel, and effective procedure for correcting this distributional shift, bringing the distribution of sparse attention outputs closer to that of quadratic attention. Our method can be applied on top of any sparse attention method, and results in an average 36%pt performance increase, recovering 88% of quadratic attention accuracy on the 131K RULER benchmark when applied on top of sliding window attention with sink tokens while only adding a small overhead. Our method can maintain approximately 98.5% sparsity over full quadratic attention, making our model 32 times faster than Flash Attention 2 when processing 1M token prefills.

We present Sphinx, a synthetic environment for visual perception and reasoning that targets core cognitive primitives. Sphinx procedurally generates puzzles using motifs, tiles, charts, icons, and geometric primitives, each paired with verifiable ground-truth solutions, enabling both precise evaluation and large-scale dataset construction. The benchmark covers 25 task types spanning symmetry detection, geometric transformations, spatial reasoning, chart interpretation, and sequence prediction. Evaluating recent large vision-language models (LVLMs) shows that even state-of-the-art GPT-5 attains only 51.1% accuracy, well below human performance. Finally, we demonstrate that reinforcement learning with verifiable rewards (RLVR) substantially improves model accuracy on these tasks and yields gains on external visual reasoning benchmarks, highlighting its promise for advancing multimodal reasoning.

DeepSeek-R1 has demonstrated remarkable effectiveness in incentivizing reasoning and generalization capabilities of large language models (LLMs) through reinforcement learning. Nevertheless, the potential of reasoning-induced computational modeling has not been thoroughly explored in the context of image quality assessment (IQA), a task critically dependent on visual reasoning. In this paper, we introduce VisualQuality-R1, a reasoning-induced no-reference IQA (NR-IQA) model, and we train it with reinforcement learning to rank, a learning algorithm tailored to the intrinsically relative nature of visual quality. Specifically, for a pair of images, we employ group relative policy optimization to generate multiple quality scores for each image. These estimates are then used to compute comparative probabilities of one image having higher quality than the other under the Thurstone model. Rewards for each quality estimate are defined using continuous fidelity measures rather than discretized binary labels. Extensive experiments show that the proposed VisualQuality-R1 consistently outperforms discriminative deep learning-based NR-IQA models as well as a recent reasoning-induced quality regression method. Moreover, VisualQuality-R1 is capable of generating contextually rich, human-aligned quality descriptions, and supports multi-dataset training without requiring perceptual scale realignment. These features make VisualQuality-R1 especially well-suited for reliably measuring progress in a wide range of image processing tasks like super-resolution and image generation.

Propelled by the rapid advancement of deep learning technologies, the YOLO series has set a new benchmark for real-time object detectors. Researchers have continuously explored innovative applications of reparameterization, efficient layer aggregation networks, and anchor-free techniques on the foundation of YOLO. To further enhance detection performance, Transformer-based structures have been introduced, significantly expanding the model's receptive field and achieving notable performance gains. However, such improvements come at a cost, as the quadratic complexity of the self-attention mechanism increases the computational burden of the model. Fortunately, the emergence of State Space Models (SSM) as an innovative technology has effectively mitigated the issues caused by quadratic complexity. In light of these advancements, we introduce Mamba-YOLO a novel object detection model based on SSM. Mamba-YOLO not only optimizes the SSM foundation but also adapts specifically for object detection tasks. Given the potential limitations of SSM in sequence modeling, such as insufficient receptive field and weak image locality, we have designed the LSBlock and RGBlock. These modules enable more precise capture of local image dependencies and significantly enhance the robustness of the model. Extensive experimental results on the publicly available benchmark datasets COCO and VOC demonstrate that Mamba-YOLO surpasses the existing YOLO series models in both performance and competitiveness, showcasing its substantial potential and competitive edge.The PyTorch code is available at:https://github.com/HZAI-ZJNU/Mamba-YOLO

While Vision Language Models (VLMs) are impressive in tasks such as visual question answering (VQA) and image captioning, their ability to apply multi-step reasoning to images has lagged, giving rise to perceptions of modality imbalance or brittleness. Towards systematic study of such issues, we introduce a synthetic framework for assessing the ability of VLMs to perform algorithmic visual reasoning (AVR), comprising three tasks: Table Readout, Grid Navigation, and Visual Analogy. Each has two levels of difficulty, SIMPLE and HARD, and even the SIMPLE versions are difficult for frontier VLMs. We seek strategies for training on the SIMPLE version of the tasks that improve performance on the corresponding HARD task, i.e., S2H generalization. This synthetic framework, where each task also has a text-only version, allows a quantification of the modality imbalance, and how it is impacted by training strategy. Ablations highlight the importance of explicit image-to-text conversion in promoting S2H generalization when using auto-regressive training. We also report results of mechanistic study of this phenomenon, including a measure of gradient alignment that seems to identify training strategies that promote better S2H generalization.

In pursuit of faster computation, Efficient Transformers demonstrate an impressive variety of approaches -- models attaining sub-quadratic attention complexity can utilize a notion of sparsity or a low-rank approximation of inputs to reduce the number of attended keys; other ways to reduce complexity include locality-sensitive hashing, key pooling, additional memory to store information in compacted or hybridization with other architectures, such as CNN. Often based on a strong mathematical basis, kernelized approaches allow for the approximation of attention with linear complexity while retaining high accuracy. Therefore, in the present paper, we aim to expand the idea of trainable kernel methods to approximate the self-attention mechanism of the Transformer architecture.

In this paper, we propose a new measure to gauge the complexity of image classification problems. Given an annotated image dataset, our method computes a complexity measure called the cumulative spectral gradient (CSG) which strongly correlates with the test accuracy of convolutional neural networks (CNN). The CSG measure is derived from the probabilistic divergence between classes in a spectral clustering framework. We show that this metric correlates with the overall separability of the dataset and thus its inherent complexity. As will be shown, our metric can be used for dataset reduction, to assess which classes are more difficult to disentangle, and approximate the accuracy one could expect to get with a CNN. Results obtained on 11 datasets and three CNN models reveal that our method is more accurate and faster than previous complexity measures.

Multi-modality foundation models, as represented by GPT-4V, have brought a new paradigm for low-level visual perception and understanding tasks, that can respond to a broad range of natural human instructions in a model. While existing foundation models have shown exciting potentials on low-level visual tasks, their related abilities are still preliminary and need to be improved. In order to enhance these models, we conduct a large-scale subjective experiment collecting a vast number of real human feedbacks on low-level vision. Each feedback follows a pathway that starts with a detailed description on the low-level visual appearance (*e.g. clarity, color, brightness* of an image, and ends with an overall conclusion, with an average length of 45 words. The constructed **Q-Pathway** dataset includes 58K detailed human feedbacks on 18,973 images with diverse low-level appearance. Moreover, to enable foundation models to robustly respond to diverse types of questions, we design a GPT-participated conversion to process these feedbacks into diverse-format 200K instruction-response pairs. Experimental results indicate that the **Q-Instruct** consistently elevates low-level perception and understanding abilities across several foundational models. We anticipate that our datasets can pave the way for a future that general intelligence can perceive, understand low-level visual appearance and evaluate visual quality like a human. Our dataset, model zoo, and demo is published at: https://q-future.github.io/Q-Instruct.

Significant advancements in Large Multimodal Models (LMMs) have enabled them to tackle complex problems involving visual-mathematical reasoning. However, their ability to identify geometric elements remains underexplored. To address this gap, we introduce Tangram, a novel benchmark designed to evaluate the performance of LMMs on geometric element recognition. Tangram comprises 1,080 diverse geometric diagrams sourced from primary and secondary school exams, competitions, and textbooks, ranging from simple geometric shapes to complex combinations. Each diagram is paired with four questions, resulting in 4,320 visual-question-answer pairs. Unlike existing benchmarks that emphasize higher-level cognition and reasoning, Tangram focuses on understanding geometric elements, requiring models to perform a ``simple yet challenging" counting task. Systematic evaluation of 13 prominent LMMs, such as GPT-4o and Claude 3.5 Sonnet, reveals that these models face significant challenges even in seemingly straightforward tasks. The top-performing model achieves an accuracy of only 53.0%, highlighting a substantial gap compared to human performance. These findings underscore the limitations of current multimodal AI systems in handling basic perception tasks and serve to inspire the development of the next generation of expert-level multimodal foundational models. The data and code will be released soon.

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

The combination of strong visual backbones and Large Language Model (LLM) reasoning has led to Large Multimodal Models (LMMs) becoming the current standard for a wide range of vision and language (VL) tasks. However, recent research has shown that even the most advanced LMMs still struggle to capture aspects of compositional visual reasoning, such as attributes and relationships between objects. One solution is to utilize scene graphs (SGs)--a formalization of objects and their relations and attributes that has been extensively used as a bridge between the visual and textual domains. Yet, scene graph data requires scene graph annotations, which are expensive to collect and thus not easily scalable. Moreover, finetuning an LMM based on SG data can lead to catastrophic forgetting of the pretraining objective. To overcome this, inspired by chain-of-thought methods, we propose Compositional Chain-of-Thought (CCoT), a novel zero-shot Chain-of-Thought prompting method that utilizes SG representations in order to extract compositional knowledge from an LMM. Specifically, we first generate an SG using the LMM, and then use that SG in the prompt to produce a response. Through extensive experiments, we find that the proposed CCoT approach not only improves LMM performance on several vision and language VL compositional benchmarks but also improves the performance of several popular LMMs on general multimodal benchmarks, without the need for fine-tuning or annotated ground-truth SGs. Code: https://github.com/chancharikmitra/CCoT

Recent advances in Large Language Models (LLMs) and Vision Language Models (VLMs) have shown significant progress in mathematical reasoning, yet they still face a critical bottleneck with problems requiring visual assistance, such as drawing auxiliary lines or plotting functions to solve the problems. Most LLMs and VLMs are constrained to text-only reasoning chains, while multimodal unified models that can generate interleaved text and images lack the necessary precision and controllability for such tasks. To address this, we propose CodePlot-CoT, a code-driven Chain-of-Thought paradigm for "thinking with images" in mathematics. Our approach leverages the VLM to generate text reasoning as well as executable plotting code, which is then rendered into images as "visual thought", to solve mathematical problems. To achieve this, we first construct Math-VR, the first large-scale, bilingual dataset and benchmark for Mathematics problems with Visual Reasoning, comprising 178K samples. Second, to create high-quality training data, we develop a state-of-the-art image-to-code converter specialized for parsing complex mathematical figures into codes. Finally, using these training data, we train the CodePlot-CoT model for solving mathematical problems. Experimental results show that our model achieves up to 21% increase over base model on our new benchmark, fully validating the efficacy of our proposed code-driven reasoning paradigm. Our work opens a new direction for multimodal mathematical reasoning and provides the community with the first large-scale dataset, comprehensive benchmark, and strong approach for such problems. To facilitate future research, we make our datasets, code, and pretrained models publicly available at https://github.com/HKU-MMLab/Math-VR-CodePlot-CoT.

The Transformer architecture, underpinned by the Multi-Head Attention (MHA) mechanism, has become the de facto standard for state-of-the-art models in artificial intelligence. However, the quadratic computational complexity of MHA with respect to sequence length presents a significant barrier to scaling, particularly for applications involving long contexts. Prevailing solutions, such as Multi-Query Attention (MQA) and Grouped-Query Attention (GQA), have effectively addressed the memory bandwidth bottleneck that dominates autoregressive inference latency by sharing Key and Value projections. While highly successful, these methods do not reduce the fundamental number of floating-point operations (FLOPs) required for the attention score computation, which remains a critical bottleneck for training and full-sequence processing. This paper introduces Sparse Query Attention (SQA), a novel attention architecture that pursues an alternative and complementary optimization path. Instead of reducing Key/Value heads, SQA reduces the number of Query heads. This architectural modification directly decreases the computational complexity of the attention mechanism by a factor proportional to the reduction in query heads, thereby lowering the overall FLOPs. This work presents the theoretical foundation of SQA, its mathematical formulation, and a family of architectural variants. Empirical benchmarks on long sequences (32k-200k tokens) demonstrate that SQA can achieve significant throughput improvements of up to 3x in computation-bound scenarios such as model pre-training, fine-tuning, and encoder-based tasks, with only a minimal impact on model quality in preliminary smallscale experiments. SQA was discovered serendipitously during the development of the upcoming Reactive Transformer architecture, suggesting its potential as a powerful tool for building more efficient and scalable models

A key frontier for Multimodal Large Language Models (MLLMs) is the ability to perform deep mathematical and spatial reasoning directly from images, moving beyond their established success in semantic description. Mathematical surface plots provide a rigorous testbed for this capability, as they isolate the task of reasoning from the semantic noise common in natural images. To measure progress on this frontier, we introduce MaRVL-QA (Mathematical Reasoning over Visual Landscapes), a new benchmark designed to quantitatively evaluate these core reasoning skills. The benchmark comprises two novel tasks: Topological Counting, identifying and enumerating features like local maxima; and Transformation Recognition, recognizing applied geometric transformations. Generated from a curated library of functions with rigorous ambiguity filtering, our evaluation on MaRVL-QA reveals that even state-of-the-art MLLMs struggle significantly, often resorting to superficial heuristics instead of robust spatial reasoning. MaRVL-QA provides a challenging new tool for the research community to measure progress, expose model limitations, and guide the development of MLLMs with more profound reasoning abilities.

Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language Models) can hardly even accurately copy a geometric figure, let alone truly understand the complex inherent logic and spatial relationships within geometric shapes. We believe accurate copying (strong perception) is the first step to visual o1. Accordingly, we introduce the concept of "slow perception" (SP), which guides the model to gradually perceive basic point-line combinations, as our humans, reconstruct complex geometric structures progressively. There are two-fold stages in SP: a) perception decomposition. Perception is not instantaneous. In this stage, complex geometric figures are broken down into basic simple units to unify geometry representation. b) perception flow, which acknowledges that accurately tracing a line is not an easy task. This stage aims to avoid "long visual jumps" in regressing line segments by using a proposed "perceptual ruler" to trace each line stroke-by-stroke. Surprisingly, such a human-like perception manner enjoys an inference time scaling law -- the slower, the better. Researchers strive to speed up the model's perception in the past, but we slow it down again, allowing the model to read the image step-by-step and carefully.