数学推理

Visual reasoning -- the ability to interpret the visual world -- is crucial for embodied agents that operate within three-dimensional scenes. Progress in AI has led to vision and language models capable of answering questions from images. However, their performance declines when tasked with 3D spatial reasoning. To tackle the complexity of such reasoning problems, we introduce an agentic program synthesis approach where LLM agents collaboratively generate a Pythonic API with new functions to solve common subproblems. Our method overcomes limitations of prior approaches that rely on a static, human-defined API, allowing it to handle a wider range of queries. To assess AI capabilities for 3D understanding, we introduce a new benchmark of queries involving multiple steps of grounding and inference. We show that our method outperforms prior zero-shot models for visual reasoning in 3D and empirically validate the effectiveness of our agentic framework for 3D spatial reasoning tasks. Project website: https://glab-caltech.github.io/vadar/

The ability of large vision-language models (LVLMs) to critique and correct their reasoning is an essential building block towards their self-improvement. However, a systematic analysis of such capabilities in LVLMs is still lacking. We propose VISCO, the first benchmark to extensively analyze the fine-grained critique and correction capabilities of LVLMs. Compared to existing work that uses a single scalar value to critique the entire reasoning [4], VISCO features **dense** and **fine-grained** critique, requiring LVLMs to evaluate the correctness of each step in the chain-of-thought and provide natural language explanations to support their judgments. Extensive evaluation of 24 LVLMs demonstrates that human-written critiques significantly enhance the performance after correction, showcasing the potential of the self-improvement strategy. However, the model-generated critiques are less helpful and sometimes detrimental to the performance, suggesting that critique is the crucial bottleneck. We identified three common patterns in critique failures: failure to critique visual perception, reluctance to "say no", and exaggerated assumption of error propagation. To address these issues, we propose an effective LookBack strategy that revisits the image to verify each piece of information in the initial reasoning. \ourscritic significantly improves critique and correction performance by up to 13.5%.

Recently, Mamba-based frameworks have achieved substantial advancements across diverse computer vision and NLP tasks, particularly in their capacity for reasoning over long-range information with linear complexity. However, the fixed 2D-to-1D scanning pattern overlooks the local structures of an image, limiting its effectiveness in aggregating 2D spatial information. While stacking additional Mamba layers can partially address this issue, it increases parameter intensity and constrains real-time application. In this work, we reconsider the local optimal scanning path in Mamba, enhancing the rigid and uniform 1D scan through the local shortest path theory, thus creating a structure-aware Mamba suited for lightweight single-image super-resolution. Specifically, we draw inspiration from the Traveling Salesman Problem (TSP) to establish a local optimal scanning path for improved structural 2D information utilization. Here, local patch aggregation occurs in a content-adaptive manner with minimal propagation cost. TSP-Mamba demonstrates substantial improvements over existing Mamba-based and Transformer-based architectures. For example, TSP-Mamba surpasses MambaIR by up to 0.7dB in lightweight SISR, with comparable parameters and very slightly extra computational demands (1-2 GFlops for 720P images).

Although large multimodal models (LMMs) have demonstrated remarkable capabilities in visual scene interpretation and reasoning, their capacity for complex and precise 3-dimensional spatial reasoning remains uncertain. Existing benchmarks focus predominantly on 2D spatial understanding and lack a framework to comprehensively evaluate 6D spatial reasoning across varying complexities.To address this limitation, we present Spatial457, a scalable and unbiased synthetic dataset designed with 4 key spatial components: multi-object recognition, 2D and 3D spatial relationships, and 3D orientation. Spatial457 supports a cascading evaluation structure, offering 7 question types across 5 difficulty levels that progress from basic single-object recognition to our newly proposed complex 6D spatial reasoning tasks.We evaluated various large multimodal models (LMMs) on Spatial457, observing a general decline in performance as task complexity increases, particularly in 3D reasoning and 6D spatial tasks. To quantify these challenges, we introduce the Relative Performance Dropping Rate (RPDR), highlighting key weaknesses in 3D reasoning capabilities. Leveraging the unbiased attribute design of our dataset, we also uncover prediction biases across different attributes, with similar patterns observed in real-world image settings.

3D affordance segmentation aims to link human instructions to touchable regions of 3D objects for embodied manipulations. Existing efforts typically adhere to single-object, single-affordance paradigms, where each affordance type or explicit instruction strictly corresponds to a specific affordance region and are unable to handle long-horizon tasks. Such a paradigm cannot actively reason about complex user intentions that often imply sequential affordances. In this paper, we introduce the Sequential 3D Affordance Reasoning task, which extends the traditional paradigm by reasoning from cumbersome user intentions and then decomposing them into a series of segmentation maps. Toward this, we construct the first instruction-based affordance segmentation benchmark that includes reasoning over both single and sequential affordances, comprising 180K instruction-point cloud pairs. Based on the benchmark, we propose our model, SeqAfford, to unlock the 3D multi-modal large language model with additional affordance segmentation abilities, which ensures reasoning with world knowledge and fine-grained affordance grounding in a cohesive framework. We further introduce a multi-granular language-point integration module to endow 3D dense prediction. Extensive experimental evaluations show that our model excels over well-established methods and exhibits open-world generalization with sequential reasoning abilities.

Due to visual ambiguities and inter-person occlusions, existing human pose estimation methods cannot recover plausible close interactions from in-the-wild videos. Even state-of-the-art large foundation models (e.g., SAM) cannot accurately distinguish human semantics in such challenging scenarios. In this work, we find that human appearance can provide a straightforward cue to address these obstacles. Based on this observation, we propose a dual-branch optimization framework to reconstruct accurate interactive motions with plausible body contacts constrained by human appearances, social proxemics, and physical laws. Specifically, we first train a diffusion model to learn the human proxemic behavior and pose prior knowledge. The trained network and two optimizable tensors are then incorporated into a dual-branch optimization framework to reconstruct human motions and appearances. Several constraints based on 3D Gaussians, 2D keypoints, and mesh penetrations are also designed to assist the optimization. With the proxemics prior and diverse constraints, our method is capable of estimating accurate interactions from in-the-wild videos captured in complex environments. We further build a dataset with pseudo ground-truth interaction annotations, which may promote future research on pose estimation and human behavior understanding. Experimental results on several benchmarks demonstrate that our method outperforms existing approaches. The code and data are available at https://www.buzhenhuang.com/works/CloseApp.html.

Current Large Multimodal Models (LMMs) empowered visual grounding typically rely on \texttt <SEG> tokens as a text prompt to jointly optimize the vision-language model (e.g., LLaVA) and the downstream task-specific model (e.g., SAM). However, we observe that little research has looked into how it works. In this work, we first visualize the similarity maps, which are obtained by computing the semantic similarity between the \texttt <SEG> token and the image token embeddings derived from the last hidden layer in both the LLaVA encoder and SAM decoder. Intriguingly, we have found that a striking consistency holds in terms of activation responses in the similarity map, which reveals that what the \texttt <SEG> token contributes to is semantic similarity within image-text pairs. Specifically, the \texttt <SEG> token, a placeholder expanded in text vocabulary, extensively queries among individual tokenized image patches to match the semantics of an object from text to the paired image, while the Large Language Models (LLMs) are being fine-tuned. Upon the above findings, we present \toolname, which facilitates LMMs' resilient REAsoning capability of where to attenD under the guidance of highly activated points borrowed from similarity maps. Remarkably, READ features an intuitive design, Similarity as Points module (SasP), which can be seamlessly applied to \texttt <SEG> -like paradigms in a plug-and-play fashion. Also, extensive experiments have been conducted on ReasonSeg and RefCOCO(+/g) datasets. To validate whether READ suffers from catastrophic forgetting of previous skills after fine-tuning, we further assess its generation ability on an augmented FP-RefCOCO(+/g) dataset. All codes and models are publicly available at \href https://github.com/rui-qian/READ https://github.com/rui-qian/READ .

Multimodal language models (MLMs) still face challenges in fundamental visual perception tasks where specialized models excel. Tasks requiring reasoning about 3D structures benefit from depth estimation, and reasoning about 2D object instances benefits from object detection. Yet, MLMs can not produce intermediate depth or boxes to reason over. Finetuning MLMs on relevant data doesn't generalize well and outsourcing computation to specialized vision tools is too compute-intensive and memory-inefficient. To address this, we introduce Perception Tokens, intrinsic image representations designed to assist reasoning tasks where language is insufficient. Perception tokens act as auxiliary reasoning tokens, akin to chain-of-thought prompts in language models. For example, in a depth-related task, an MLM augmented with perception tokens can reason by generating a depth map as tokens, enabling it to solve the problem effectively. We propose AURORA, a training method that augments MLMs with perception tokens for improved reasoning over visual inputs. AUROA leverages a VQVAE to transform intermediate image representations, such as depth maps into a tokenized format and bounding box tokens, which is then used in a multi-task training framework. AURORA achieves notable improvements across counting benchmarks: +10.8% on BLINK, +11.3% on CVBench, and +8.3% on SEED-Bench, outperforming finetuning approaches in generalization across datasets. It also improves on relative depth: over +6% on BLINK. With perception tokens, AURORA expands the scope of MLMs beyond language-based reasoning, paving the way for more effective visual reasoning capabilities. Code and data will be released at the https://aurora-perception.github.io.

We tackle the problem of automatic calibration of radially distorted cameras in challenging conditions. Accurately determining distortion parameters typically requires either 1) solving the full Structure from Motion (SfM) problem involving camera poses, 3D points, and the distortion parameters, which is only possible if many images with sufficient overlap are provided, or 2) relying heavily on learning-based methods that are comparatively less accurate. In this work, we demonstrate that distortion calibration can be decoupled from 3D reconstruction, maintaining the accuracy of SfM-based methods while avoiding many of the associated complexities. This is achieved by working in Projective Space, where the geometry is unique up to a homography, which encapsulates all camera parameters except for distortion. Our proposed method, Projective Radial Distortion Averaging, averages multiple distortion estimates in a fully projective framework without creating 3d points and full bundle adjustment. By relying on pairwise projective relations, our methods support any feature-matching approaches without constructing point tracks across multiple images.

Multimodal Large Language Models (MLLMs) have shown promising capabilities in mathematical reasoning within visual contexts across various datasets. However, most existing multimodal math benchmarks are limited to single-visual contexts, which diverges from the multi-visual scenarios commonly encountered in real-world mathematical applications. To address this gap, we introduce MV-MATH: a meticulously curated dataset of 2,009 high-quality mathematical problems. Each problem integrates multiple images interleaved with text, derived from authentic K-12 scenarios and enriched with detailed annotations. MV-MATH includes multiple-choice, free-form, and multi-step questions, covering 11 subject areas across 3 difficulty levels, and serves as a comprehensive and rigorous benchmark for assessing MLLMs' mathematical reasoning in multi-visual contexts. Through extensive experimentation, we observe that MLLMs encounter substantial challenges in multi-visual math tasks, with a considerable performance gap relative to human capabilities on MV-MATH. Furthermore, we analyze the performance and error patterns of various models, providing insights into MLLMs' mathematical reasoning capabilities within multi-visual settings.

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems.

We propose novel fast algorithms for the Gromov--Wasserstein problem (GW) with cyclic symmetry of input data. This problem naturally appears as an object-matching task, which underlies various real-world computer vision applications, e.g., image registration, point cloud registration, stereo matching, and 3D reconstruction. Gradient-based algorithms have been widely used to solve GW, and our main idea is to utilize the following remarkable property that emerges in GW with cyclic symmetry: By setting the initial solution to have cyclic symmetry, all intermediate solutions and matrices that appear in the gradient-based algorithms have the same cyclic symmetry until convergence. Based on this property, our gradient-based algorithms restrict the solution space to have cyclic symmetry and update only one symmetric part of solutions and matrices at each iteration, resulting in faster computation. Moreover, our algorithms solve the optimal transport problem at each iteration, which also exhibits cyclic symmetry. This problem can be solved efficiently, and as a result, our algorithms perform significantly faster. Experiments showed the effectiveness of our algorithms in synthetic and real-world data with strict and approximate cyclic symmetry.

Scene generation with 3D assets presents a complex challenge, requiring both high-level semantic understanding and low-level geometric reasoning. While Multimodal Large Language Models (MLLMs) excel at semantic tasks, their application to 3D scene generation is hindered by their limited grounding on 3D geometry. In this paper, we investigate how to best work with MLLMs in an object placement task. Towards this goal, we introduce a novel framework, FirePlace, that applies existing MLLMs in (1) 3D geometric reasoning and the extraction of relevant geometric details from the 3D scene, (2) constructing and solving geometric constraints on the extracted low-level geometry, and (3) pruning for final placements that conform to common sense. By combining geometric reasoning with real-world understanding of MLLMs, our method can propose object placements that satisfy both geometric constraints as well as high-level semantic common-sense considerations. Our experiments show that these capabilities allow our method to place objects more effectively in complex scenes with intricate geometry, surpassing the quality of prior work.

Deep saliency models, which predict what parts of an image capture our attention, are often like black boxes. This limits their use, especially in areas where understanding why a model makes a decision is crucial. Our research tackles this challenge by developing an explainable saliency (XSal) model that not only identifies what is important in an image, but also explains its choices in a way that makes sense to humans. We achieve this by using vision-language models to reason about images and by focusing the model's attention on the most crucial information using a contextual prioritization mechanism. Unlike prior approaches that rely on fixation descriptions or soft-attention based semantic aggregation, our method directly models the reasoning steps involved in saliency prediction, generating selectively prioritized explanations clarify why specific regions are prioritized. Comprehensive evaluations demonstrate the effectiveness of our model in generating high-quality saliency maps and coherent, contextually relevant explanations. This research is a step towards more transparent and trustworthy AI systems that can help us understand and navigate the world around us.

Multimodal language models (MLLMs) are increasingly being applied in real-world environments, necessitating their ability to interpret 3D spaces and comprehend temporal dynamics. Current methods often rely on specialized architectural designs or task-specific fine-tuning to achieve this. We introduce Coarse Correspondences, a simple lightweight method that enhances MLLMs' spatial-temporal reasoning with 2D images as input, without modifying the architecture or requiring task-specific fine-tuning. Our method uses a lightweight tracking model to identify primary object correspondences between frames in a video or across different image viewpoints, and then conveys this information to MLLMs through visual prompting. We demonstrate that this simple training-free approach brings substantial gains to GPT4-V/O consistently on four benchmarks that require spatial-temporal reasoning, including +20.5% improvement on ScanQA, +9.7% on OpenEQA's episodic memory subset, +6.0% on the long-form video benchmark EgoSchema, and +11% on the R2R navigation benchmark. Additionally, we show that Coarse Correspondences can also enhance open-source MLLMs' spatial reasoning (by +6.9% on ScanQA) when applied in both training and inference and that the improvement can generalize to unseen datasets such as SQA3D (+3.1%). Taken together, we show that Coarse Correspondences effectively and efficiently boosts models' performance on downstream tasks requiring spatial-temporal reasoning.

Finding semantic correspondences between images is a challenging problem in computer vision, particularly under significant viewpoint changes. Previous methods rely on semantic features from pre-trained 2D models like Stable Diffusion and DINOv2, which often struggle to extract viewpoint-invariant features. To overcome this, we propose a novel approach that integrates geometric and semantic reasoning. Unlike prior methods relying on heuristic geometric enhancements, our framework fine-tunes DUSt3R on synthetic cross-instance data to reconstruct distinct objects in an aligned 3D space. By learning to deform these objects into similar shapes using semantic supervision, we enable efficient KNN-based geometric matching, followed by sparse semantic matching within local KNN candidates. While trained on synthetic data, our method generalizes effectively to real-world images, achieving up to 7.4-point improvements in zero-shot settings on the rigid-body subset of Spair-71K and up to 19.6-point gains under extreme viewpoint variations. Additionally, it accelerates runtime by up to 40 times, demonstrating both its robustness to viewpoint changes and its efficiency for practical applications.

The commonsense reasoning capabilities of vision-language models (VLMs), especially in abductive reasoning and defeasible reasoning, remain poorly understood. Most benchmarks focus on typical visual scenarios, making it difficult to discern whether model performance stems from keen perception and reasoning skills, or reliance on pure statistical recall. We argue that by focusing on atypical events in videos, clearer insights can be gained on the core capabilities of VLMs. Explaining and understanding such out-of-distribution events requires models to extend beyond basic pattern recognition and regurgitation of their prior knowledge. To this end, we introduce BlackSwanSuite, a benchmark for evaluating VLMs' ability to reason about unexpected events through abductive and defeasible tasks. Our tasks artificially limit the amount of visual information provided to models while questioning them about hidden unexpected events, or provide new visual information that could change an existing hypothesis about the event. We curate a comprehensive benchmark suite comprising over 3,800 MCQ, 4,900 generative and 6,700 yes/no questions, spanning 1,655 videos. After extensively evaluating various state-of-the-art VLMs, including GPT-4o and Gemini 1.5 Pro, as well as open-source VLMs such as LLaVA-Video, we find significant performance gaps of up to 32% from humans on these tasks. Our findings reveal key limitations in current VLMs, emphasizing the need for enhanced model architectures and training strategies. Our data and leaderboard is available at blackswan.cs.ubc.ca.

Constructing compact and informative 3D scene representations is essential for effective embodied exploration and reasoning, especially in complex environments over extended periods. Existing representations, such as object-centric 3D scene graphs, oversimplify spatial relationships by modeling scenes as isolated objects with restrictive textual relationships, making it difficult to address queries requiring nuanced spatial understanding. Moreover, these representations lack natural mechanisms for active exploration and memory management, hindering their application to lifelong autonomy. In this work, we propose 3D-Mem, a novel 3D scene memory framework for embodied agents. 3D-Mem employs informative multi-view images, termed Memory Snapshots, to capture rich visual information of explored regions. It further integrates frontier-based exploration by introducing Frontier Snapshots--glimpses of unexplored areas--enabling agents to make decisions by considering both known and potential new information. To support lifelong memory in active exploration settings, we present an incremental construction pipeline for 3D-Mem, as well as a memory retrieval technique for memory management. Experimental results on three benchmarks demonstrate that 3D-Mem significantly enhances agents' exploration and reasoning capabilities in 3D environments, highlighting its potential for advancing applications in embodied AI.