Daily Papers

Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable: a relation expressed in textual reasoning or drawing code carries no guarantee that a constraint-satisfying configuration realizes it. We observe that existing externalization methods based on rendered pixels or one-shot scripts fail to provide exact, per-action geometric guarantees. Enforcing geometric relations by algebraic definition closes this gap: the workspace becomes a constraint-checked evolving canvas. We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine. In a Propose-Draw-Verify loop, Draw2Think externalizes hypotheses onto an executable canvas, measures exact geometric quantities, and feeds structured observations back to the model, so subsequent reasoning proceeds from checked canvas state grounded by the shared workspace. This externalization makes two properties separately auditable: model-level Construction Fidelity (whether the canvas realizes the intended configuration) and engine-level Measurement Faithfulness (exact values and relations from canvas constraints). Across construction, outcome, and rendering evaluations, Draw2Think builds canvases that pass 95.9% predicate-level and 84.0% strict problem-level construction checks on GeoGoal, improves outcome accuracy by up to 4.1%/16.4% on planar/solid benchmarks, and attains 68.2%/90.5% strict/relaxed rendering scores on GenExam-math. Project page is available at https://draw2think.github.io/

Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry.

Recent approaches on visual scene understanding attempt to build a scene graph -- a computational representation of objects and their pairwise relationships. Such rich semantic representation is very appealing, yet difficult to obtain from a single image, especially when considering complex spatial arrangements in the scene. Differently, an image sequence conveys useful information using the multi-view geometric relations arising from camera motion. Indeed, in such cases, object relationships are naturally related to the 3D scene structure. To this end, this paper proposes a system that first computes the geometrical location of objects in a generic scene and then efficiently constructs scene graphs from video by embedding such geometrical reasoning. Such compelling representation is obtained using a new model where geometric and visual features are merged using an RNN framework. We report results on a dataset we created for the task of 3D scene graph generation in multiple views.

LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely using natural language. Dedicated domain-specific languages like Lean provide clear supervision via formal verification of proofs, enabling effective training through reinforcement learning. In this work, we propose Seed-Prover, a lemma-style whole-proof reasoning model. Seed-Prover can iteratively refine its proof based on Lean feedback, proved lemmas, and self-summarization. To solve IMO-level contest problems, we design three test-time inference strategies that enable both deep and broad reasoning. Seed-Prover proves 78.1% of formalized past IMO problems, saturates MiniF2F, and achieves over 50\% on PutnamBench, outperforming the previous state-of-the-art by a large margin. To address the lack of geometry support in Lean, we introduce a geometry reasoning engine Seed-Geometry, which outperforms previous formal geometry engines. We use these two systems to participate in IMO 2025 and fully prove 5 out of 6 problems. This work represents a significant advancement in automated mathematical reasoning, demonstrating the effectiveness of formal verification with long chain-of-thought reasoning.

We present layered ray intersections (LaRI), a new method for unseen geometry reasoning from a single image. Unlike conventional depth estimation that is limited to the visible surface, LaRI models multiple surfaces intersected by the camera rays using layered point maps. Benefiting from the compact and layered representation, LaRI enables complete, efficient, and view-aligned geometric reasoning to unify object- and scene-level tasks. We further propose to predict the ray stopping index, which identifies valid intersecting pixels and layers from LaRI's output. We build a complete training data generation pipeline for synthetic and real-world data, including 3D objects and scenes, with necessary data cleaning steps and coordination between rendering engines. As a generic method, LaRI's performance is validated in two scenarios: It yields comparable object-level results to the recent large generative model using 4% of its training data and 17% of its parameters. Meanwhile, it achieves scene-level occluded geometry reasoning in only one feed-forward.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. To ensure syntactic correctness and geometric consistency, we propose a training paradigm that combines Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs' capabilities for downstream geometry reasoning tasks. Our data and code are available at Geoparsing.

In this paper, we introduce a novel geometry-aware self-training framework for room layout estimation models on unseen scenes with unlabeled data. Our approach utilizes a ray-casting formulation to aggregate multiple estimates from different viewing positions, enabling the computation of reliable pseudo-labels for self-training. In particular, our ray-casting approach enforces multi-view consistency along all ray directions and prioritizes spatial proximity to the camera view for geometry reasoning. As a result, our geometry-aware pseudo-labels effectively handle complex room geometries and occluded walls without relying on assumptions such as Manhattan World or planar room walls. Evaluation on publicly available datasets, including synthetic and real-world scenarios, demonstrates significant improvements in current state-of-the-art layout models without using any human annotation.

Spatial consistency is a fundamental property of the visual world and a key requirement for models that aim to understand physical reality. Despite recent advances, multimodal large language models (MLLMs) often struggle to reason about 3D geometry across multiple views. Rather than asking models to describe scene attributes, we introduce a more challenging task: given two views of the same scene, identify the object that violates 3D motion consistency. We propose a simple and scalable method for generating realistic, spatially inconsistent image pairs from multi-view scenes, enabling systematic evaluation of this capability. Our results show that state-of-the-art MLLMs significantly underperform human observers and exhibit substantial variability across different scene attributes, revealing a fragile and incomplete understanding of 3D structure. We hope our findings underscore the need for approaches that develop a more deeply grounded understanding of the physical world.

Vision language models (VLMs) are expected to perform effective multimodal reasoning and make logically coherent decisions, which is critical to tasks such as diagram understanding and spatial problem solving. However, current VLM reasoning lacks large-scale and well-structured training datasets. To bridge this gap, we propose VisualSphinx, a first-of-its-kind large-scale synthetic visual logical reasoning training data. To tackle the challenge of image synthesis with grounding answers, we propose a rule-to-image synthesis pipeline, which extracts and expands puzzle rules from seed questions and generates the code of grounding synthesis image synthesis for puzzle sample assembly. Experiments demonstrate that VLM trained using GRPO on VisualSphinx benefit from logical coherence and readability of our dataset and exhibit improved performance on logical reasoning tasks. The enhanced reasoning capabilities developed from VisualSphinx also benefit other reasoning tasks such as algebraic reasoning, arithmetic reasoning and geometry reasoning.

We present PVSeRF, a learning framework that reconstructs neural radiance fields from single-view RGB images, for novel view synthesis. Previous solutions, such as pixelNeRF, rely only on pixel-aligned features and suffer from feature ambiguity issues. As a result, they struggle with the disentanglement of geometry and appearance, leading to implausible geometries and blurry results. To address this challenge, we propose to incorporate explicit geometry reasoning and combine it with pixel-aligned features for radiance field prediction. Specifically, in addition to pixel-aligned features, we further constrain the radiance field learning to be conditioned on i) voxel-aligned features learned from a coarse volumetric grid and ii) fine surface-aligned features extracted from a regressed point cloud. We show that the introduction of such geometry-aware features helps to achieve a better disentanglement between appearance and geometry, i.e. recovering more accurate geometries and synthesizing higher quality images of novel views. Extensive experiments against state-of-the-art methods on ShapeNet benchmarks demonstrate the superiority of our approach for single-image novel view synthesis.

Multimodal Chain-of-Thought (CoT) reasoning requires large vision-language models to construct reasoning trajectories that interleave perceptual grounding with multi-step inference. However, existing Reinforcement Learning with Verifiable Rewards (RLVR) methods typically optimize reasoning at a coarse granularity, treating CoT uniformly without distinguishing their varying degrees of visual grounding. In this work, we conduct a token-level analysis of multimodal reasoning trajectories and show that successful reasoning is characterized by structured token dynamics reflecting both perceptual grounding and exploratory inference. Building upon this analysis, we propose Perception-Exploration Policy Optimization (PEPO), which derives a perception prior from hidden state similarity and integrates it with token entropy through a smooth gating mechanism to produce token-level advantages. PEPO integrates seamlessly with existing RLVR frameworks such as GRPO and DAPO, requiring neither additional supervision nor auxiliary branches. Extensive experiments across diverse multimodal benchmarks demonstrate consistent and robust improvements over strong RL baselines, spanning geometry reasoning, visual grounding, visual puzzle solving, and few-shot classification, while maintaining stable training dynamics. Code: https://github.com/xzxxntxdy/PEPO

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomenon, offering a new lens for interpretability and formal analysis of LLMs' behavior.

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models' proficiency in reasoning-based geometry-where solutions are derived using algebraic methods-NoReGeo focuses on evaluating whether LLMs can inherently encode spatial relationships and recognize geometric properties directly. Our benchmark comprises 2,500 trivial geometric problems spanning 25 categories, each carefully crafted to be solvable purely through native geometric understanding, assuming known object locations. We assess a range of state-of-the-art models on NoReGeo, including frontier models like GPT-4, observing that even the most advanced systems achieve an overall maximum of 65% accuracy in binary classification tasks. Further, our ablation experiments demonstrate that such geometric understanding does not emerge through fine-tuning alone, indicating that effective training for geometric comprehension requires a specialized approach from the outset. Our findings highlight a significant gap in current LLMs' ability to natively grasp geometric concepts, providing a foundation for future research toward models with true geometric cognition.

A defining feature of human intelligence is the ability to adapt to changing environments by inferring latent task structure from sparse observations. Neuroscientific research indicates that this capability relies on the hippocampus constructing abstract representations, expressed as low-dimensional, approximately orthogonal manifolds in neural state space. However, the internal mechanisms of large language models (LLMs) remain largely opaque, making it unclear whether they form comparable abstract representations or instead rely on task-specific statistical regularities when performing comparable reasoning tasks. Here we adapt a contextual reversal-learning paradigm to a text-based setting and compare humans and LLMs at both the Behavioural and representational levels. We report that although LLMs exhibit generalizable reasoning less frequently than humans, when such inference occurs, their internal states exhibit abstract geometric structures that resemble those reported in the hippocampus. Notably, this representational geometry is not uniformly distributed but is organized hierarchically across model depth: whereas lower layers show early, stable encoding of stimulus identity, higher layers form a hippocampal-like functional band enriched for abstract context geometry associated with inference. Furthermore, complementary intervention experiments mechanistically implicate geometry in reasoning: task-sequence language modelling induces geometric disentanglement, whereas geometric regularization of higher layers increases the emergence of generalizable inference. Together, these findings establish abstract representational geometry as a mechanistic principle supporting inference in large language models.

We present S1-VL, a multimodal reasoning model for scientific domains that natively supports two complementary reasoning paradigms: Scientific Reasoning, which relies on structured chain-of-thought, and Thinking-with-Images, which enables the model to actively manipulate images through Python code execution during reasoning. In the Thinking-with-Images mode, the model generates and executes image-processing code in a sandbox environment, obtains intermediate visual results, and continues reasoning in a multi-turn iterative manner. This design is particularly effective for challenging scenarios such as high-resolution scientific chart interpretation, microscopic image understanding, and geometry-assisted reasoning. To construct the training data, we collect scientific multimodal datasets spanning six disciplines: mathematics, physics, chemistry, astronomy, geography, and biology. We further develop a six-dimensional quality filtering framework for reasoning trajectories. To mitigate redundant, ineffective, and erroneous visual operations commonly found in existing datasets, we propose a multi-stage filtering pipeline together with an adaptive data routing strategy. This strategy converts samples with low visual information gain into pure Reasoning-mode data, enabling the model to learn when image operations are truly necessary. S1-VL is trained through a four-stage progressive pipeline: scientific multimodal SFT, Thinking-with-Images cold-start SFT, and two stages of reinforcement learning with SAPO. We build S1-VL-32B on top of Qwen3-VL-32B-Thinking and evaluate it on 13 benchmarks. Experimental results show that S1-VL-32B achieves state-of-the-art performance on all five Thinking-with-Images benchmarks, including HRBench-4K, HRBench-8K, MME-RealWorld-CN, MME-RealWorld-Lite, and V*, and outperforms compared systems on scientific reasoning benchmarks such as Physics and VRSBench.

We present JoyAI-Image, a unified multimodal foundation model for visual understanding, text-to-image generation, and instruction-guided image editing. JoyAI-Image couples a spatially enhanced Multimodal Large Language Model (MLLM) with a Multimodal Diffusion Transformer (MMDiT), allowing perception and generation to interact through a shared multimodal interface. Around this architecture, we build a scalable training recipe that combines unified instruction tuning, long-text rendering supervision, spatially grounded data, and both general and spatial editing signals. This design gives the model broad multimodal capability while strengthening geometry-aware reasoning and controllable visual synthesis. Experiments across understanding, generation, long-text rendering, and editing benchmarks show that JoyAI-Image achieves state-of-the-art or highly competitive performance. More importantly, the bidirectional loop between enhanced understanding, controllable spatial editing, and novel-view-assisted reasoning enables the model to move beyond general visual competence toward stronger spatial intelligence. These results suggest a promising path for unified visual models in downstream applications such as vision-language-action systems and world models.

Equation discovery from data is a core challenge in machine learning for science, requiring the recovery of concise symbolic expressions that govern complex physical and geometric phenomena. Recent approaches with large language models (LLMs) show promise in symbolic regression, but their success often hinges on memorized formulas or overly simplified functional forms. Existing benchmarks exacerbate this limitation: they focus on scalar functions, ignore domain grounding, and rely on brittle string-matching based metrics that fail to capture scientific equivalence. We introduce SurfaceBench, first comprehensive benchmark for symbolic surface discovery. SurfaceBench comprises 183 tasks across 15 categories of symbolic complexity, spanning explicit, implicit, and parametric equation representation forms. Each task includes ground-truth equations, variable semantics, and synthetically sampled three dimensional data. Unlike prior SR datasets, our tasks reflect surface-level structure, resist LLM memorization through novel symbolic compositions, and are grounded in scientific domains such as fluid dynamics, robotics, electromagnetics, and geometry. To evaluate equation discovery quality, we pair symbolic checks with geometry-aware metrics such as Chamfer and Hausdorff distances, capturing both algebraic fidelity and spatial reconstruction accuracy. Our experiments reveal that state-of-the-art frameworks, while occasionally successful on specific families, struggle to generalize across representation types and surface complexities. SurfaceBench thus establishes a challenging and diagnostic testbed that bridges symbolic reasoning with geometric reconstruction, enabling principled benchmarking of progress in compositional generalization, data-driven scientific induction, and geometry-aware reasoning with LLMs. We release the code here: https://github.com/Sanchit-404/surfacebench

The integration of geometric reconstruction and generative modeling remains a critical challenge in developing AI systems capable of human-like spatial reasoning. This paper proposes Aether, a unified framework that enables geometry-aware reasoning in world models by jointly optimizing three core capabilities: (1) 4D dynamic reconstruction, (2) action-conditioned video prediction, and (3) goal-conditioned visual planning. Through task-interleaved feature learning, Aether achieves synergistic knowledge sharing across reconstruction, prediction, and planning objectives. Building upon video generation models, our framework demonstrates unprecedented synthetic-to-real generalization despite never observing real-world data during training. Furthermore, our approach achieves zero-shot generalization in both action following and reconstruction tasks, thanks to its intrinsic geometric modeling. Remarkably, even without real-world data, its reconstruction performance far exceeds that of domain-specific models. Additionally, Aether leverages a geometry-informed action space to seamlessly translate predictions into actions, enabling effective autonomous trajectory planning. We hope our work inspires the community to explore new frontiers in physically-reasonable world modeling and its applications.

This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding space when answering logical comparison questions (e.g., Was Cristiano born before Messi?). We first identified these subspaces using partial least squares regression, which effectively encodes the numerical attributes associated with the entities in comparison prompts. Further, we demonstrate causality by intervening in these subspaces to manipulate hidden states, thereby altering the LLM's comparison outcomes. Experimental results show that our findings hold for different numerical attributes, indicating that LLMs utilize the linearly encoded information for numerical reasoning.

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Large vision language models exhibit notable limitations on Geometry Problem Solving (GPS) because of their unreliable diagram interpretation and pure natural-language reasoning. A recent line of work mitigates this by using symbolic solvers: the model directly generates a formal program that a geometry solver can execute. However, this direct program generation lacks intermediate reasoning, making the decision process opaque and prone to errors. In this work, we explore a new approach that integrates Chain-of-Thought (CoT) with formal language. The model interleaves natural language reasoning with incremental emission of solver-executable code, producing a hybrid reasoning trace in which critical derivations are expressed in formal language. To teach this behavior at scale, we combine (1) supervised fine-tuning on an 11K newly developed synthetic dataset with interleaved natural language reasoning and automatic formalization, and (2) solver-in-the-loop reinforcement learning that jointly optimizes both the CoT narrative and the resulting program through outcome-based rewards. Built on Qwen2.5-VL-7B, our new model, named GF-Reasoner, achieves up to 15% accuracy improvements on standard GPS benchmarks, surpassing both 7B-scale peers and the much larger model Qwen2.5-VL-72B. By exploiting high-order geometric knowledge and offloading symbolic computation to the solver, the generated reasoning traces are noticeably shorter and cleaner. Furthermore, we present a comprehensive analysis of method design choices (e.g., reasoning paradigms, data synthesis, training epochs, etc.), providing actionable insights for future research.

As LLMs advance their reasoning capabilities about the physical world, the absence of rigorous benchmarks for evaluating their ability to generate scientifically valid physical models has become a critical gap. Computational mechanics, which develops and applies mathematical models and numerical methods to predict the behavior of physical systems under forces, deformation, and constraints, provides an ideal foundation for structured scientific reasoning evaluation. Problems follow clear mathematical structure, enforce strict physical and numerical constraints, and support objective verification. The discipline requires constructing explicit models of physical systems and reasoning about geometry, spatial relationships, and material behavior, connecting directly to emerging AI goals in physical reasoning and world modeling. We introduce FEM-Bench, a computational mechanics benchmark designed to evaluate the ability of LLMs to generate correct finite element method (FEM) and related code. FEM-Bench 2025 contains a suite of introductory but nontrivial tasks aligned with material from a first graduate course on computational mechanics. These tasks capture essential numerical and physical modeling challenges while representing only a small fraction of the complexity present in the discipline. Despite their simplicity, state-of-the-art LLMs do not reliably solve all of them. In a five attempt run, the best performing model at function writing, Gemini 3 Pro, completed 30/33 tasks at least once and 26/33 tasks all five times. The best performing model at unit test writing, GPT-5, had an Average Joint Success Rate of 73.8%. Other popular models showed broad performance variation. FEM-Bench establishes a structured foundation for evaluating AI-generated scientific code, and future iterations will incorporate increasingly sophisticated tasks to track progress as models evolve.

Recent advancements in Large Vision-Language Models have showcased remarkable capabilities. However, they often falter when confronted with complex reasoning tasks that humans typically address through visual aids and deliberate, step-by-step thinking. While existing methods have explored text-based slow thinking or rudimentary visual assistance, they fall short of capturing the intricate, interleaved nature of human visual-verbal reasoning processes. To overcome these limitations and inspired by the mechanisms of slow thinking in human cognition, we introduce VisuoThink, a novel framework that seamlessly integrates visuospatial and linguistic domains. VisuoThink facilitates multimodal slow thinking by enabling progressive visual-textual reasoning and incorporates test-time scaling through look-ahead tree search. Extensive experiments demonstrate that VisuoThink significantly enhances reasoning capabilities via inference-time scaling, even without fine-tuning, achieving state-of-the-art performance in tasks involving geometry and spatial reasoning.

Realistic and efficient 3D garment generation remains a longstanding challenge in computer vision and digital fashion. Existing methods typically rely on large vision- language models to produce serialized representations of 2D sewing patterns, which are then transformed into simulation-ready 3D meshes using garment modeling framework such as GarmentCode. Although these approaches yield high-quality results, they often suffer from slow inference times, ranging from 30 seconds to a minute. In this work, we introduce SwiftTailor, a novel two-stage framework that unifies sewing-pattern reasoning and geometry-based mesh synthesis through a compact geometry image representation. SwiftTailor comprises two lightweight modules: PatternMaker, an efficient vision-language model that predicts sewing patterns from diverse input modalities, and GarmentSewer, an efficient dense prediction transformer that converts these patterns into a novel Garment Geometry Image, encoding the 3D surface of all garment panels in a unified UV space. The final 3D mesh is reconstructed through an efficient inverse mapping process that incorporates remeshing and dynamic stitching algorithms to directly assemble the garment, thereby amortizing the cost of physical simulation. Extensive experiments on the Multimodal GarmentCodeData demonstrate that SwiftTailor achieves state-of-the-art accuracy and visual fidelity while significantly reducing inference time. This work offers a scalable, interpretable, and high-performance solution for next-generation 3D garment generation.

Multimodal large language models (MLLMs) are increasingly being applied to spatial cognition tasks, where they are expected to understand and interact with complex environments. Most existing works improve spatial reasoning by introducing 3D priors or geometric supervision, which enhances performance but incurs substantial data preparation and alignment costs. In contrast, purely 2D approaches often struggle with multi-frame spatial reasoning due to their limited ability to capture cross-frame spatial relationships. To address these limitations, we propose EgoMind, a Chain-of-Thought framework that enables geometry-free spatial reasoning through Role-Play Caption, which jointly constructs a coherent linguistic scene graph across frames, and Progressive Spatial Analysis, which progressively reasons toward task-specific questions. With only 5K auto-generated SFT samples and 20K RL samples, EgoMind achieves competitive results on VSI-Bench, SPAR-Bench, SITE-Bench, and SPBench, demonstrating its effectiveness in strengthening the spatial reasoning capabilities of MLLMs and highlighting the potential of linguistic reasoning for spatial cognition. Code and data are released at https://github.com/Hyggge/EgoMind.

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3,113 real-world K-12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference efficiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence.

How do reasoning models verify their own answers? We study this question by training a model using DeepSeek R1's recipe on the CountDown task. We leverage the fact that preference tuning leads to mode collapse, yielding a model that always produces highly structured chain-of-thought sequences. With this setup, we do top-down and bottom-up analyses to reverse-engineer how the model verifies its outputs. Top-down, we find Gated Linear Unit (GLU) weights encoding verification-related tokens, such as ``success'' or ``incorrect''. Bottom-up, we find that ``previous-token heads'' are mainly responsible for self-verification in our setup. Our analyses meet in the middle: drawing inspiration from inter-layer communication channels, we use the identified GLU weights to localize as few as three attention heads that can disable self-verification, pointing to a necessary component of a potentially larger verification circuit. Finally, we verify that similar verification components exist in our base model and a general reasoning DeepSeek-R1 model.

Solving Algebra Problems with Geometry Diagrams (APGDs) is still a challenging problem because diagram processing is not studied as intensively as language processing. To work against this challenge, this paper proposes a hologram reasoning scheme and develops a high-performance method for solving APGDs by using this scheme. To reach this goal, it first defines a hologram, being a kind of graph, and proposes a hologram generator to convert a given APGD into a hologram, which represents the entire information of APGD and the relations for solving the problem can be acquired from it by a uniform way. Then HGR, a hologram reasoning method employs a pool of prepared graph models to derive algebraic equations, which is consistent with the geometric theorems. This method is able to be updated by adding new graph models into the pool. Lastly, it employs deep reinforcement learning to enhance the efficiency of model selection from the pool. The entire HGR not only ensures high solution accuracy with fewer reasoning steps but also significantly enhances the interpretability of the solution process by providing descriptions of all reasoning steps. Experimental results demonstrate the effectiveness of HGR in improving both accuracy and interpretability in solving APGDs.

Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs. Nevertheless, we observe that naive token fusion followed by standard fine-tuning in this line of work often leaves such geometric cues underutilized for spatial reasoning, as VLMs tend to rely heavily on 2D visual cues. In this paper, we propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens. GeoSR introduces two key components: (1) Geometry-Unleashing Masking, which strategically masks portions of 2D vision tokens during training to weaken non-geometric shortcuts and force the model to consult geometry tokens for spatial reasoning; and (2) Geometry-Guided Fusion, a gated routing mechanism that adaptively amplifies geometry token contributions in regions where geometric evidence is critical. Together, these designs unleash the potential of geometry tokens for spatial reasoning tasks. Extensive experiments on both static and dynamic spatial reasoning benchmarks demonstrate that GeoSR consistently outperforms prior methods and establishes new state-of-the-art performance by effectively leveraging geometric information. The project page is available at https://suhzhang.github.io/GeoSR/.

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

Recent progress in spatial reasoning with Multimodal Large Language Models (MLLMs) increasingly leverages geometric priors from 3D encoders. However, most existing integration strategies remain passive: geometry is exposed as a global stream and fused in an indiscriminate manner, which often induces semantic-geometry misalignment and redundant signals. We propose GeoThinker, a framework that shifts the paradigm from passive fusion to active perception. Instead of feature mixing, GeoThinker enables the model to selectively retrieve geometric evidence conditioned on its internal reasoning demands. GeoThinker achieves this through Spatial-Grounded Fusion applied at carefully selected VLM layers, where semantic visual priors selectively query and integrate task-relevant geometry via frame-strict cross-attention, further calibrated by Importance Gating that biases per-frame attention toward task-relevant structures. Comprehensive evaluation results show that GeoThinker sets a new state-of-the-art in spatial intelligence, achieving a peak score of 72.6 on the VSI-Bench. Furthermore, GeoThinker demonstrates robust generalization and significantly improved spatial perception across complex downstream scenarios, including embodied referring and autonomous driving. Our results indicate that the ability to actively integrate spatial structures is essential for next-generation spatial intelligence. Code can be found at https://github.com/Li-Hao-yuan/GeoThinker.

Solid geometry problem solving demands spatial mathematical reasoning that integrates spatial intelligence and symbolic reasoning. However, most existing multimodal mathematical reasoning benchmarks focus primarily on 2D plane geometry, rely on static datasets prone to data contamination and memorization, and evaluate models solely by final answers, overlooking the reasoning process. To address these limitations, we introduce DynaSolidGeo, the first dynamic benchmark for evaluating genuine spatial reasoning in Vision-Language Models (VLMs). Constructed through a semi-automatic annotation pipeline, DynaSolidGeo contains 503 expert-curated seed questions that can, in principle, dynamically generate an unbounded number of diverse multimodal text-visual instances. Beyond answer accuracy, we incorporate process evaluation based on expert-annotated reasoning chains to measure logical validity and causal coherence. Experiments across representative open-source and closed-source VLMs reveal large performance gaps, severe degradation in dynamic settings, and poor performance on tasks requiring high-level spatial intelligence, such as mental rotation and visualization. The code and dataset are available at https://zgca-ai4edu.github.io/DynaSolidGeo/{DynaSolidGeo}.

Background: The deployment of personalized Large Language Models (LLMs) is currently constrained by the stability-plasticity dilemma. Prevailing alignment methods, such as Supervised Fine-Tuning (SFT), rely on stochastic weight updates that often incur an "alignment tax" -- degrading general reasoning capabilities. Methods: We propose the Soul Engine, a framework based on the Linear Representation Hypothesis, which posits that personality traits exist as orthogonal linear subspaces. We introduce SoulBench, a dataset constructed via dynamic contextual sampling. Using a dual-head architecture on a frozen Qwen-2.5 base, we extract disentangled personality vectors without modifying the backbone weights. Results: Our experiments demonstrate three breakthroughs. First, High-Precision Profiling: The model achieves a Mean Squared Error (MSE) of 0.011 against psychological ground truth. Second, Geometric Orthogonality: T-SNE visualization confirms that personality manifolds are distinct and continuous, allowing for "Zero-Shot Personality Injection" that maintains original model intelligence. Third, Deterministic Steering: We achieve robust control over behavior via vector arithmetic, validated through extensive ablation studies. Conclusion: This work challenges the necessity of fine-tuning for personalization. By transitioning from probabilistic prompting to deterministic latent intervention, we provide a mathematically rigorous foundation for safe, controllable AI personalization.

Plane geometry problem solving (PGPS) has recently gained significant attention as a benchmark to assess the multi-modal reasoning capabilities of large vision-language models. Despite the growing interest in PGPS, the research community still lacks a comprehensive overview that systematically synthesizes recent work in PGPS. To fill this gap, we present a survey of existing PGPS studies. We first categorize PGPS methods into an encoder-decoder framework and summarize the corresponding output formats used by their encoders and decoders. Subsequently, we classify and analyze these encoders and decoders according to their architectural designs. Finally, we outline major challenges and promising directions for future research. In particular, we discuss the hallucination issues arising during the encoding phase within encoder-decoder architectures, as well as the problem of data leakage in current PGPS benchmarks.

In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

Vision-Language Models (VLMs) still lack robustness in spatial intelligence, demonstrating poor performance on spatial understanding and reasoning tasks. We attribute this gap to the absence of a visual geometry learning process capable of reconstructing 3D space from 2D images. We present G^2VLM, a geometry grounded vision-language model that bridges two fundamental aspects of spatial intelligence: spatial 3D reconstruction and spatial understanding. G^2VLM natively leverages learned 3D visual geometry features to directly predict 3D attributes and enhance spatial reasoning tasks via in-context learning and interleaved reasoning. Our unified design is highly scalable for spatial understanding: it trains on abundant multi-view image and video data, while simultaneously leveraging the benefits of 3D visual priors that are typically only derived from hard-to-collect annotations. Experimental results demonstrate G^2VLM is proficient in both tasks, achieving comparable results to state-of-the-art feed-forward 3D reconstruction models and achieving better or competitive results across spatial understanding and reasoning tasks. By unifying a semantically strong VLM with low-level 3D vision tasks, we hope G^2VLM can serve as a strong baseline for the community and unlock more future applications, such as 3D scene editing.

Large vision-language models (VLMs) still struggle with reliable 3D spatial reasoning, a core capability for embodied and physical AI systems. This limitation arises from their inability to capture fine-grained 3D geometry and spatial relationships. While recent efforts have introduced multi-view geometry transformers into VLMs, they typically fuse only the deep-layer features from vision and geometry encoders, discarding rich hierarchical signals and creating a fundamental bottleneck for spatial understanding. To overcome this, we propose SpatialStack, a general hierarchical fusion framework that progressively aligns vision, geometry, and language representations across the model hierarchy. Moving beyond conventional late-stage vision-geometry fusion, SpatialStack stacks and synchronizes multi-level geometric features with the language backbone, enabling the model to capture both local geometric precision and global contextual semantics. Building upon this framework, we develop VLM-SpatialStack, a model that achieves state-of-the-art performance on multiple 3D spatial reasoning benchmarks. Extensive experiments and ablations demonstrate that our multi-level fusion strategy consistently enhances 3D understanding and generalizes robustly across diverse spatial reasoning tasks, establishing SpatialStack as an effective and extensible design paradigm for vision-language-geometry integration in next-generation multimodal physical AI systems.

Large Vision-Language Models (LVLMs) hold great promise for advancing remote sensing (RS) analysis, yet existing reasoning segmentation frameworks couple linguistic reasoning and pixel prediction through end-to-end supervised fine-tuning, leading to weak geometric grounding and limited generalization across tasks. To address this, we developed Think2Seg-RS, a decoupled framework that trains an LVLM prompter to control a frozen Segment Anything Model (SAM) via structured geometric prompts. Through a mask-only reinforcement learning objective, the LVLM learns to translate abstract semantic reasoning into spatially grounded actions, achieving state-of-the-art performance on the EarthReason dataset. Remarkably, the learned prompting policy generalizes zero-shot to multiple referring segmentation benchmarks, exposing a distinct divide between semantic-level and instance-level grounding. We further found that compact segmenters outperform larger ones under semantic-level supervision, and that negative prompts are ineffective in heterogeneous aerial backgrounds. Together, these findings establish semantic-level reasoning segmentation as a new paradigm for geospatial understanding, opening the way toward unified, interpretable LVLM-driven Earth observation. Our code and model are available at https://github.com/Ricardo-XZ/Think2Seg-RS.

6D object pose estimation, which predicts the transformation of an object relative to the camera, remains challenging for unseen objects. Existing approaches typically rely on explicitly constructing feature correspondences between the query image and either the object model or template images. In this work, we propose PoseGAM, a geometry-aware multi-view framework that directly predicts object pose from a query image and multiple template images, eliminating the need for explicit matching. Built upon recent multi-view-based foundation model architectures, the method integrates object geometry information through two complementary mechanisms: explicit point-based geometry and learned features from geometry representation networks. In addition, we construct a large-scale synthetic dataset containing more than 190k objects under diverse environmental conditions to enhance robustness and generalization. Extensive evaluations across multiple benchmarks demonstrate our state-of-the-art performance, yielding an average AR improvement of 5.1% over prior methods and achieving up to 17.6% gains on individual datasets, indicating strong generalization to unseen objects. Project page: https://windvchen.github.io/PoseGAM/ .

Visual Language Models (VLMs) have increasingly become the main paradigm for understanding indoor scenes, but they still struggle with metric and spatial reasoning. Current approaches rely on end-to-end video understanding or large-scale spatial question answering fine-tuning, inherently coupling perception and reasoning. In this paper, we investigate whether decoupling perception and reasoning leads to improved spatial reasoning. We propose an agentic framework for static 3D indoor scene reasoning that grounds an LLM in an explicit 3D scene graph (3DSG). Rather than ingesting videos directly, each scene is represented as a persistent 3DSG constructed by a dedicated perception module. To isolate reasoning performance, we instantiate the 3DSG from ground-truth annotations. The agent interacts with the scene exclusively through structured geometric tools that expose fundamental properties such as object dimensions, distances, poses, and spatial relationships. The results we obtain on the static split of VSI-Bench provide an upper bound under ideal perceptual conditions on the spatial reasoning performance, and we find that it is significantly higher than previous works, by up to 16\%, without task specific fine-tuning. Compared to base VLMs, our agentic variant achieves significantly better performance, with average improvements between 33\% to 50\%. These findings indicate that explicit geometric grounding substantially improves spatial reasoning performance, and suggest that structured representations offer a compelling alternative to purely end-to-end visual reasoning.

Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs).To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. To enable the model to acquire and apply Euclidean principles from these geometry problems, we employed Group Relative Policy Optimization (GRPO) to finetune the Qwen2.5VL family and RoboBrain2.0 family, inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy of all evaluated models rose from 34.5% to 40.5%, improving by 5.5 percentage points. Among them, RoboBrain2.0-Euclid-7B achieves 49.6\% accuracy, surpassing the previous state-of-the-art model, Spatial-MLLM.To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in https://zgca-ai4edu.github.io/Euclids_Gift.

Omni-directional (360°) cameras provide embodied agents with a holistic view of their surroundings, making them suited for directional reasoning in tasks such as navigation and object search. Existing Vision Language Models (VLMs) project 360° observations to 2D equirectangular projection (ERP) images and process them using architectures designed for perspective images. However, they ignore the spherical nature of 360° observations, where each pixel represents a viewing direction relative to the agent. Consequently, their direction estimates often become inconsistent under camera view transformations caused by agent motion. This limitation is particularly critical for map-free navigation, where the agent must continuously estimate the target direction in its egocentric frame. We propose EAGOR, a training-free, geometry-aware framework for embodied 360° directional reasoning. Instead of predicting target directions as ERP image coordinates, EAGOR formulates directional reasoning as recursive Bayesian estimation directly on the sphere. It maintains a continuous belief over target directions and propagates it equivariantly under agent motion without training the backbone VLMs. To achieve this, we introduce the Spherical Harmonic Belief Field (SH-BF), whose spherical harmonic representation provides a globally defined, rotation-aware basis for directional estimation on the spherical manifold. This formulation eliminates ERP seam discontinuities, latitude distortions, and interpolation errors. We evaluate EAGOR on two benchmark datasets and real-world experiments with a legged robot across directional reasoning tasks. EAGOR consistently outperforms existing methods, achieving average relative gains of +34.4% and +45.6% on HOS and OSR-Bench, respectively, while improving navigation success by +14.6%, reducing step count by 17.7%, and lowering mean angular error by 24.5%.

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's foundational logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. We open source the theorem library and the benchmark of LeanGeo at https://github.com/project-numina/LeanGeo/tree/master.

State-of-the-art embedding models are increasingly derived from decoder-only Large Language Model (LLM) backbones adapted via contrastive learning. Given the emergence of reasoning models trained via Reinforcement Learning with Verifiable Rewards (RLVR), a natural question arises: do enhanced reasoning translate to superior semantic representations when these models serve as embedding initializations? Contrary to expectation, our evaluation on MTEB and BRIGHT reveals a **null effect**: embedding models initialized from RLVR-tuned backbones yield no consistent performance advantage over their base counterparts when subjected to identical training recipes. To unpack this paradox, we introduce **H**ierarchical **R**epresentation **S**imilarity **A**nalysis (HRSA), a framework that decomposes similarity across representation, geometry, and function levels. HRSA reveals that while RLVR induces irreversible latent manifold's local geometry reorganization and reversible coordinate basis drift, it preserves the global manifold geometry and linear readout. Consequently, subsequent contrastive learning drives strong alignment between base- and reasoning-initialized models, a phenomenon we term **Manifold Realignment**. Empirically, our findings suggest that unlike Supervised Fine-Tuning (SFT), RLVR optimizes trajectories within an existing semantic landscape rather than fundamentally restructuring the landscape itself.

Understanding how transformer representations evolve across layers, not merely what they encode, remains an open problem in mechanistic interpretability. We recast the transformer forward pass as a discrete population trajectory through a high-dimensional representation manifold, drawing on geometric tools from computational neuroscience. Rather than probing for pre-specified features, we characterize trajectory geometry using five metrics computed directly in the ambient space: trajectory length, curvature, a semantic convergence index, layerwise cosine similarity, and representational stability. Across three model families (GPT-2, TinyLlama, Qwen2.5) and five controlled prompt families, we report four findings. First, semantically related prompts converge significantly in middle-to-late layers (peak CI 0.41--0.58, p<0.001, Mann-Whitney U), consistent with attractor-like dynamics. Second, reasoning tasks produce trajectories of greater curvature than lexical variations (0.71--0.83 rad vs. 0.27--0.31 rad), suggesting curvature encodes computational complexity. Third, ambiguous tokens exhibit trajectory bifurcation with up to 5.6x representational separation by the final layer, absent in unambiguous controls. Fourth, layerwise cosine similarity reveals a universal three-phase structure: encoding, elaboration, and output preparation, consistent across all three architectures. All four effects vanish under shuffled-layer and random-embedding controls. We release a fully open-source, model-agnostic pipeline and argue that trajectory geometry constitutes a principled, probe-free lens for mechanistic interpretability.

Monocular and stereo depth estimation offer complementary strengths: monocular methods capture rich contextual priors but lack geometric precision, while stereo approaches leverage epipolar geometry yet struggle with ambiguities such as reflective or textureless surfaces. Despite post-hoc synergies, these paradigms remain largely disjoint in practice. We introduce a unified framework that bridges both through iterative bidirectional alignment of their latent representations. At its core, a novel cross-attentive alignment mechanism dynamically synchronizes monocular contextual cues with stereo hypothesis representations during stereo reasoning. This mutual alignment resolves stereo ambiguities (e.g., specular surfaces) by injecting monocular structure priors while refining monocular depth with stereo geometry within a single network. Extensive experiments demonstrate state-of-the-art results: it reduces zero-shot generalization error by !>!40% on Middlebury and ETH3D, while addressing longstanding failures on transparent and reflective surfaces. By harmonizing multi-view geometry with monocular context, our approach enables robust 3D perception that transcends modality-specific limitations. Codes available at https://github.com/aeolusguan/BridgeDepth.

Geometry problem solving is a key area of mathematical reasoning, which is widely involved in many important fields such as education, mathematical ability assessment of artificial intelligence, and multimodal ability assessment. In recent years, the rapid development of deep learning technology, especially the rise of multimodal large language models, has triggered a widespread research boom. This paper provides a survey of the applications of deep learning in geometry problem solving, including (i) a comprehensive summary of the relevant tasks in geometry problem solving; (ii) a thorough review of related deep learning methods; (iii) a detailed analysis of evaluation metrics and methods; and (iv) a critical discussion of the current challenges and future directions that can be explored. Our goal is to provide a comprehensive and practical reference of deep learning for geometry problem solving to promote further developments in this field. We create a continuously updated list of papers on GitHub: https://github.com/majianz/dl4gps.

Vision-language models (VLMs) can couple visual perception with open-ended clinical reasoning, making them attractive for computational histopathology. However, fine-tuning billions of parameters on scarce, expert-annotated pathology data is prohibitive, while in-context learning (ICL), which conditions the VLM on demonstrative image-text pairs without parameter updates, suffers from high sensitivity to which examples are selected and how the query is phrased, producing unreliable diagnostics. Existing selection strategies rely on query-dependent nearest-neighbour retrieval that ignores global data structure, require costly parameter updates, or disregard the joint vision-text embedding geometry of VLMs. We propose GAUC, a training-free coreset selection method operating directly in the pre-trained multimodal embedding space. GAUC jointly optimises three objectives: (1) a Maximum Mean Discrepancy term enforcing distributional fidelity between coreset and full dataset, (2) an Effective Mutual Information Difference regulariser bounding performance degradation under prompt paraphrases by exploiting the VLM's joint vision-text alignment, and (3) a predictive-variance penalty suppressing overconfident, unstable outputs. On CRC-100K and MHIST across multiple open-source VLM architectures, GAUC consistently improves accuracy, calibration, and prompt robustness over recent ICL selection methods and dataset-distillation baselines, all without a single gradient update.

Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning ability in this task through accurate identification and adaptive application of geometric principles within visual contexts. However, existing benchmarks fail to jointly assess both dimensions of the human-like geometric reasoning mechanism in MLLMs, remaining a critical gap in assessing their ability to tackle GPS. To this end, we introduce GeoSense, the first comprehensive bilingual benchmark designed to systematically evaluate the geometric reasoning abilities of MLLMs through the lens of geometric principles. GeoSense features a five-level hierarchical framework of geometric principles spanning plane and solid geometry, an intricately annotated dataset of 1,789 problems, and an innovative evaluation strategy. Through extensive experiments on GeoSense with various open-source and closed-source MLLMs, we observe that Gemini-2.0-pro-flash performs best, achieving an overall score of 65.3. Our in-depth analysis reveals that the identification and application of geometric principles remain a bottleneck for leading MLLMs, jointly hindering their reasoning abilities. These findings underscore GeoSense's potential to guide future advancements in MLLMs' geometric reasoning capabilities, paving the way for more robust and human-like reasoning in artificial intelligence.

Accurate spatial reasoning in outdoor environments - covering geometry, object pose, and inter-object relationships - is fundamental to downstream tasks such as mapping, motion forecasting, and high-level planning in autonomous driving. We introduce SURDS, a large-scale benchmark designed to systematically evaluate the spatial reasoning capabilities of vision language models (VLMs). Built on the nuScenes dataset, SURDS comprises 41,080 vision-question-answer training instances and 9,250 evaluation samples, spanning six spatial categories: orientation, depth estimation, pixel-level localization, pairwise distance, lateral ordering, and front-behind relations. We benchmark leading general-purpose VLMs, including GPT, Gemini, and Qwen, revealing persistent limitations in fine-grained spatial understanding. To address these deficiencies, we go beyond static evaluation and explore whether alignment techniques can improve spatial reasoning performance. Specifically, we propose a reinforcement learning-based alignment scheme leveraging spatially grounded reward signals - capturing both perception-level accuracy (location) and reasoning consistency (logic). We further incorporate final-answer correctness and output-format rewards to guide fine-grained policy adaptation. Our GRPO-aligned variant achieves an overall score of 40.80 in the SURDS benchmark. Notably, it outperforms proprietary systems such as GPT-4o (13.30) and Gemini-2.0-flash (35.71). To our best knowledge, this is the first study to demonstrate that reinforcement learning-based alignment can significantly and consistently enhance the spatial reasoning capabilities of VLMs in real-world driving contexts. We release the SURDS benchmark, evaluation toolkit, and GRPO alignment code through: https://github.com/XiandaGuo/Drive-MLLM.

General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties, while simultaneously preserving its fine-grained appearance details. Recent approaches derive semantic embeddings and integrate them into advanced diffusion models to enable geometry-editable generation. However, these highly compact embeddings encode only high-level semantic cues and inevitably discard fine-grained appearance details. We introduce a Disentangled Geometry-editable and Appearance-preserving Diffusion (DGAD) model that first leverages semantic embeddings to implicitly capture the desired geometric transformations and then employs a cross-attention retrieval mechanism to align fine-grained appearance features with the geometry-edited representation, facilitating both precise geometry editing and faithful appearance preservation in object composition. Specifically, DGAD builds on CLIP/DINO-derived and reference networks to extract semantic embeddings and appearance-preserving representations, which are then seamlessly integrated into the encoding and decoding pipelines in a disentangled manner. We first integrate the semantic embeddings into pre-trained diffusion models that exhibit strong spatial reasoning capabilities to implicitly capture object geometry, thereby facilitating flexible object manipulation and ensuring effective editability. Then, we design a dense cross-attention mechanism that leverages the implicitly learned object geometry to retrieve and spatially align appearance features with their corresponding regions, ensuring faithful appearance consistency. Extensive experiments on public benchmarks demonstrate the effectiveness of the proposed DGAD framework.

Video spatial reasoning is essential for navigation-oriented perception and long-video question answering, where models must infer spatial relations across long horizons under changing viewpoints. However, existing multimodal large language models (MLLMs) remain largely semantic-centric, and often fail to reliably aggregate consistent spatial evidence from redundant video observations, leading to inefficient or unstable reasoning. To address these issues, we propose ConsiSpace, a geometry-consistency-aware framework for geometry-sensitive video spatial reasoning that turns spatial consistency into both an evidence organization principle and an explicit post-SFT learning signal. We build a geometry-consistent memory (GCM) including implicit evidence tokens and explicit geometric cues, and leverage efficient organization strategies to compactly preserve task-related spatial evidence. Furthermore, we utilize unified consistency self-supervised reinforcement learning (UC-SSRL) after supervised fine-tuning to improve cross-view stability, with answer-, metric-, and topology-consistency rewards. Extensive experiments on three spatial-reasoning benchmarks, VSI-Bench, OSI-Bench, and MMSI-Video-Bench, show consistent gains, improving the average score by 12.6 points over the strongest baselines.

Discrete motion tokenization has recently enabled Large Language Models (LLMs) to serve as versatile backbones for motion understanding and motion-language reasoning. However, existing pipelines typically decouple motion quantization from semantic embedding learning, linking them solely via token IDs. This approach fails to effectively align the intrinsic geometry of the motion space with the embedding space, thereby hindering the LLM's capacity for nuanced motion reasoning. We argue that alignment is most effective when both modalities share a unified geometric basis. Therefore, instead of forcing the LLM to reconstruct the complex geometry among motion tokens from scratch, we present a novel framework that explicitly enforces orthogonality on both the motion codebook and the LLM embedding space, ensuring that their relational structures naturally mirror each other. Specifically, we employ a decoder-only quantizer with Gumbel-Softmax for differentiable training and balanced codebook usage. To bridge the modalities, we use a sparse projection that maps motion codes into the LLM embedding space while preserving orthogonality. Finally, a two-stage orthonormal regularization schedule enforces soft constraints during tokenizer training and LLM fine-tuning to maintain geometric alignment without hindering semantic adaptation. Extensive experiments on HumanML3D demonstrate that our framework achieves a 20% performance improvement over current state-of-the-art methods, validating that a unified geometric basis effectively empowers the LLM for nuanced motion reasoning.

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

Understanding and reasoning about the physical world requires spatial intelligence: the ability to interpret geometry, perspective, and spatial relations beyond 2D perception. While recent vision large models (VLMs) excel at visual understanding, they remain fundamentally 2D perceivers and struggle with genuine 3D reasoning. We introduce Think3D, a framework that enables VLM agents to think with 3D space. By leveraging 3D reconstruction models that recover point clouds and camera poses from images or videos, Think3D allows the agent to actively manipulate space through camera-based operations and ego/global-view switching, transforming spatial reasoning into an interactive 3D chain-of-thought process. Without additional training, Think3D significantly improves the spatial reasoning performance of advanced models such as GPT-4.1 and Gemini 2.5 Pro, yielding average gains of +7.8% on BLINK Multi-view and MindCube, and +4.7% on VSI-Bench. We further show that smaller models, which struggle with spatial exploration, benefit significantly from a reinforcement learning policy that enables the model to select informative viewpoints and operations. With RL, the benefit from tool usage increases from +0.7% to +6.8%. Our findings demonstrate that training-free, tool-augmented spatial exploration is a viable path toward more flexible and human-like 3D reasoning in multimodal agents, establishing a new dimension of multimodal intelligence. Code and weights are released at https://github.com/zhangzaibin/spagent.

Precise spatial understanding from multi-view images remains a fundamental challenge for Multimodal Large Language Models (MLLMs), as their visual representations are predominantly semantic and lack explicit geometric grounding. While existing approaches augment visual tokens with geometric cues from visual geometry models, their MLLM is still required to implicitly infer the underlying 3D structure of the scene from these augmented tokens, limiting its spatial reasoning capability. To address this issue, we introduce Cog3DMap, a framework that recurrently constructs an explicit 3D memory from multi-view images, where each token is grounded in 3D space and possesses both semantic and geometric information. By feeding these tokens into the MLLM, our framework enables direct reasoning over a spatially structured 3D map, achieving state-of-the-art performance on various spatial reasoning benchmarks. Code will be made publicly available.

Video spatial reasoning requires accumulating viewpoint-dependent evidence over time while retaining information useful to the question being asked. Existing spatial video-language models improve geometric perception and long-range context modeling, but often treat memory as a generic temporal cache, which can introduce redundant or irrelevant geometry and weaken long-horizon reasoning. We propose \ours, a question-guided geometric memory framework for video spatial reasoning. \ours injects camera-conditioned geometry into visual tokens and maintains two complementary memories: a Fine-Grained Context Bank for recent dense features and camera states, and a Semantic-Geometric Evidence Bank for compact long-range evidence. Each candidate frame is scored by the product of Q-Former-based question relevance and novelty with respect to the retained bank; this score is stored and reused during reading, while a capacity-based replacement rule keeps the bank compact. During reasoning, both memories are read before update and adaptively fused with the current frame representation. Experiments on VSI-Bench and VSTI-Bench show that \ours achieves state-of-the-art performance among evaluated spatial reasoning models, validating the effectiveness of question-guided geometric memory. Ablations further verify the contribution of the proposed evidence scoring mechanism.

Vision-Language Models have achieved strong progress in ground-view visual understanding, yet they remain brittle in high-altitude Unmanned Aerial Vehicle scenes, where objects are tiny and densely packed, textures are repetitive, and top-down orientations are ambiguous. We introduce UAVReason, a large-scale UAV-native dataset and evaluation suite for studying unified aerial reasoning and generation under this nadir-view domain shift. UAVReason aligns RGB imagery, depth maps, semantic segmentation masks, captions, and question-answer pairs within a consistent aerial domain. It contains 23.6K captioned frames, 273K VQA pairs including 68.2K two-frame temporal questions, and 188.8K cross-modal generation samples across RGB, depth, and segmentation modalities. We further adapt UAVReason-Bagel as a unified understanding-and-generation baseline that jointly optimizes language reasoning and dense visual generation objectives. Experiments show that general-purpose VLMs and off-the-shelf unified generators struggle with UAV-native grounding, while UAVReason-Bagel substantially improves over its pretrained counterpart, increasing VQA-1F F1 from 0.394 to 0.711, VQA-2F F1 from 0.427 to 0.822, and heading-aware VQA F1 from 0.798 to 0.973. For generation, it improves segmentation mIoU to 0.143 and reduces KID from 0.078 to 0.048 for depth-segmentation-text-conditioned RGB synthesis. More importantly, our ablations reveal a bidirectional synergy between synthesis and reasoning. Dense generation objectives improve temporal semantic consistency, while language-level reasoning regularizes sparse-condition image synthesis. These results suggest that unified reasoning and generation provide effective geometry-aware structural priors for physically grounded aerial intelligence. All data, code, and evaluation tools will be released.

We discover that large language models exhibit spectral phase transitions in their hidden activation spaces when engaging in reasoning versus factual recall. Through systematic spectral analysis across 11 models spanning 5 architecture families (Qwen, Pythia, Phi, Llama, DeepSeek-R1), we identify seven core phenomena: (1)~Reasoning Spectral Compression -- 9/11 models show significantly lower α for reasoning (p < 0.05), with larger effects in stronger models; (2)~Instruction Tuning Spectral Reversal -- base models show reasoning α< factual α, while instruction-tuned models reverse this relationship; (3)~Architecture-Dependent Generation Taxonomy -- prompt-to-response shifts partition into expansion, compression, and equilibrium regimes; (4)~Spectral Scaling Law -- α_reasoning propto -0.074 ln N across 4 Qwen base models (R^2 = 0.46); (5)~Token-Level Spectral Cascade -- per-token alpha tracking reveals local synchronization that decays exponentially with layer distance, and is weaker for reasoning than factual tasks; (6)~Reasoning Step Spectral Punctuation -- phase-transition signatures align with reasoning step boundaries; and (7)~Spectral Correctness Prediction -- spectral α alone achieves AUC = 1.000 (Qwen2.5-7B, late layers) and mean AUC = 0.893 across 6 models in predicting correctness before the final answer is generated. Together, these findings establish a comprehensive spectral theory of reasoning in transformers, revealing that the geometry of thought is universal in direction, architecture-specific in dynamics, and predictive of outcome.

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness and contractivity assumptions, a generalized update scheme not only unifies classical methods such as mirror descent and dynamic programming but also captures modern chain-of-thought reasoning processes in large language models. In particular, we prove that our accelerated iterative update achieves an O(1/t^2) convergence rate in the absence of persistent perturbations, and we further demonstrate that feedback (iterative) architectures are necessary to approximate certain fixed-point functions efficiently. These theoretical insights bridge classical acceleration techniques with contemporary applications in neural computation and optimization.

Recovering the 3D scene geometry from a single view is a fundamental yet ill-posed problem in computer vision. While classical depth estimation methods infer only a 2.5D scene representation limited to the image plane, recent approaches based on radiance fields reconstruct a full 3D representation. However, these methods still struggle with occluded regions since inferring geometry without visual observation requires (i) semantic knowledge of the surroundings, and (ii) reasoning about spatial context. We propose KYN, a novel method for single-view scene reconstruction that reasons about semantic and spatial context to predict each point's density. We introduce a vision-language modulation module to enrich point features with fine-grained semantic information. We aggregate point representations across the scene through a language-guided spatial attention mechanism to yield per-point density predictions aware of the 3D semantic context. We show that KYN improves 3D shape recovery compared to predicting density for each 3D point in isolation. We achieve state-of-the-art results in scene and object reconstruction on KITTI-360, and show improved zero-shot generalization compared to prior work. Project page: https://ruili3.github.io/kyn.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in 2D visual tasks but still exhibit limited physical spatial awareness when processing real-world visual streams. Recently, feed-forward geometric foundation models, which implicitly extract geometric priors, have provided a new pathway to address this issue. However, existing geometry-aware MLLMs are predominantly constrained by the paradigm of single deep-layer extraction and input-level fusion. This flattened fusion leads to the loss of local geometric details and causes semantic mismatches in the early layers. To break this bottleneck, we propose GUIDE (Geometric Unrolling Inside MLLM Early-layers), a progressive geometric priors injection framework. GUIDE performs multi-level sampling within the geometric encoder, comprehensively capturing multi-granularity features ranging from local edges to global topologies. Subsequently, we rigorously align and fuse these multi-level geometric priors step-by-step with the early layers of the MLLM. Building upon the injection of multi-granularity geometric information, this design guides the model to progressively learn the 2D-to-3D transitional process. Furthermore, we introduce a context-aware gating that enables the model to fetch requisite spatial cues based on current semantics, thereby maximizing the utilization efficiency of spatial priors and effectively suppressing redundant geometric noise. Extensive experiments demonstrate that GUIDE significantly outperforms existing baselines on multiple complex spatial reasoning and perception tasks, establishing a novel paradigm for integrating 3D geometric priors into large models.

Evaluating the symbolic reasoning of large language models (LLMs) calls for geometry benchmarks that require multi-step proofs grounded in both text and diagrams. However, existing benchmarks are often limited in scale and rarely provide visually grounded multiple-choice questions, limiting reliable evaluation of complex reasoning. We introduce GeoChallenge, a dataset of 90K automatically generated multiple-choice geometry proof problems, each requiring multi-step reasoning over aligned textual descriptions and diagrams. GeoChallenge provides fine-grained complexity ratings and formal language annotations to enable controlled evaluation. Experiments on multiple advanced LLMs show a clear performance gap between models and humans (the best-performing model, GPT-5-nano, achieves 75.89 exact match vs. 94.74 for humans). Further analysis also reveals three common failure patterns of LLMs: (1) exact match failures under the multiple-choice setting; (2) weak visual reliance; and (3) overextended reasoning without convergence.

Open-Vocabulary 3D object affordance grounding aims to anticipate ``action possibilities'' regions on 3D objects with arbitrary instructions, which is crucial for robots to generically perceive real scenarios and respond to operational changes. Existing methods focus on combining images or languages that depict interactions with 3D geometries to introduce external interaction priors. However, they are still vulnerable to a limited semantic space by failing to leverage implied invariant geometries and potential interaction intentions. Normally, humans address complex tasks through multi-step reasoning and respond to diverse situations by leveraging associative and analogical thinking. In light of this, we propose GREAT (GeometRy-intEntion collAboraTive inference) for Open-Vocabulary 3D Object Affordance Grounding, a novel framework that mines the object invariant geometry attributes and performs analogically reason in potential interaction scenarios to form affordance knowledge, fully combining the knowledge with both geometries and visual contents to ground 3D object affordance. Besides, we introduce the Point Image Affordance Dataset v2 (PIADv2), the largest 3D object affordance dataset at present to support the task. Extensive experiments demonstrate the effectiveness and superiority of GREAT. The code and dataset are available at https://yawen-shao.github.io/GREAT/.

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.

Reconstructing articulated 3D objects from a single image requires jointly inferring object geometry, part structure, and motion parameters from limited visual evidence. A key difficulty lies in the entanglement between motion cues and object structure, which makes direct articulation regression unstable. Existing methods address this challenge through multi-view supervision, retrieval-based assembly, or auxiliary video generation, often sacrificing scalability or efficiency. We present MonoArt, a unified framework grounded in progressive structural reasoning. Rather than predicting articulation directly from image features, MonoArt progressively transforms visual observations into canonical geometry, structured part representations, and motion-aware embeddings within a single architecture. This structured reasoning process enables stable and interpretable articulation inference without external motion templates or multi-stage pipelines. Extensive experiments on PartNet-Mobility demonstrate that OM achieves state-of-the-art performance in both reconstruction accuracy and inference speed. The framework further generalizes to robotic manipulation and articulated scene reconstruction.

"Thinking with images" has emerged as an effective paradigm for advancing visual reasoning, extending beyond text-only chains of thought by injecting visual evidence into intermediate reasoning steps. However, existing methods fall short of human-like abstract visual thinking, as their flexibility is fundamentally limited by external tools. In this work, we introduce Monet, a training framework that enables multimodal large language models (MLLMs) to reason directly within the latent visual space by generating continuous embeddings that function as intermediate visual thoughts. We identify two core challenges in training MLLMs for latent visual reasoning: high computational cost in latent-vision alignment and insufficient supervision over latent embeddings, and address them with a three-stage distillation-based supervised fine-tuning (SFT) pipeline. We further reveal a limitation of applying GRPO to latent reasoning: it primarily enhances text-based reasoning rather than latent reasoning. To overcome this, we propose VLPO (Visual-latent Policy Optimization), a reinforcement learning method that explicitly incorporates latent embeddings into policy gradient updates. To support SFT, we construct Monet-SFT-125K, a high-quality text-image interleaved CoT dataset containing 125K real-world, chart, OCR, and geometry CoTs. Our model, Monet-7B, shows consistent gains across real-world perception and reasoning benchmarks and exhibits strong out-of-distribution generalization on challenging abstract visual reasoning tasks. We also empirically analyze the role of each training component and discuss our early unsuccessful attempts, providing insights for future developments in visual latent reasoning. Our model, data, and code are available at https://github.com/NOVAglow646/Monet.

Structured images (e.g., charts and geometric diagrams) remain challenging for multimodal large language models (MLLMs), as perceptual slips can cascade into erroneous conclusions. Intermediate visual cues can steer reasoning; however, existing cue-based methods are constrained with low-fidelity image processing and linear, rigid reasoning patterns, limiting their effectiveness on complex structured-image tasks. In this paper, we propose PixelCraft, a novel multi-agent system for high-fidelity image processing and flexible visual reasoning on structured images. The system comprises a dispatcher, a planner, a reasoner, critics, and a set of visual tool agents. To achieve high-fidelity processing, we construct a high-quality corpus and fine-tune an MLLM into a grounding model, whose pixel-level localizations are integrated with traditional computer vision (CV) algorithms in tool agents. Building on this foundation, PixelCraft facilitates flexible visual reasoning through a dynamic three-stage workflow of tool selection, agent discussion, and self-criticism. Moreover, unlike prior linear reasoning patterns that simply append historical images, PixelCraft maintains an image memory to allow the planner to adaptively revisit earlier visual steps, explore alternative reasoning branches, and dynamically adjust the reasoning trajectory during discussion. Extensive experiments on challenging chart and geometry benchmarks demonstrate that PixelCraft significantly improves visual reasoning performance for advanced MLLMs, setting a new standard for structured image reasoning. Our code will be available at https://github.com/microsoft/PixelCraft.

Reinforcement learning (RL) is a central approach for improving reasoning capabilities in large language models (LLMs), where training efficiency depends critically on how problems are sampled during optimization. Existing adaptive curriculum learning methods typically prioritize prompts of intermediate difficulty, treating problem selection as a standard bandit problem with independent arms and overlooking the structured, heterogeneous nature of the task space. In this work, we frame problem sampling as a manifold-structured bandit problem with endogenous non-stationarity: problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space. To operationalize this perspective, we introduce Bayesian Manifold Curriculum (BMC), a structure-aware framework that organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling. Empirically, we find that different sampling strategies induce non-trivial tradeoffs between productivity (learning signal), diversity (coverage of the task manifold), and utility (evaluation relevance). These results show that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Despite significant progress in Vision-Language Navigation (VLN), existing approaches still rely on dense RGB videos that produce excessive patch tokens and lack explicit spatial structure, resulting in substantial computational overhead and limited spatial reasoning. To address these issues, we introduce the Geometry-Aware BEV (GA-BEV) - a compact, 3D-grounded feature representation that integrates both explicit and implicit geometric cues into multimodal large language model (MLLM) - based navigation systems. We construct BEV spatial maps from RGB-D inputs by projecting visual features into 3D space and aggregating them into an agent-centric layout that preserves geometric consistency while reducing token redundancy. To further enrich geometric understanding, we incorporate features from a pretrained 3D foundation model into the BEV space, injecting structural priors learned from large-scale 3D reconstruction tasks. Together, these complementary cues - explicit depth-based projection and implicit learned priors - yield compact yet spatially expressive representations that substantially improve navigation efficiency and performance. Experiments show that our method achieves state-of-the-art results using only navigation data, without DAgger augmentation or mixed VQA training, demonstrating the robustness and data efficiency of the proposed GA-VLN framework.

Neural representations carry rich geometric structure; but does that structure causally shape behavior? To address this question, we intervene along paths through activation space defined by different geometries, and measure the behavioral trajectories they induce. In particular, we test whether interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturally. Concretely, we first fit an activation manifold M_h to representations and a behavior manifold M_y to output probability distributions. We then test the link M_h leftrightarrow M_y via interventions: we find that steering along M_h, which we term manifold steering, yields behavioral trajectories that follow M_y, while linear steering -- which assumes a Euclidean geometry -- cuts through off-manifold regions and hence produces unnatural outputs. Moreover, optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h. We demonstrate this bidirectional relationship between the geometry of representation and behavior across tasks and modalities. In language models, we use reasoning tasks with cyclic and sequential geometries as well as in-context learning tasks with more complex graph geometries. In a video world model, we use a task with geometry corresponding to physical dynamics. Overall, our work shows that geometry in neural representation is not merely incidental, but is in fact the proper object for enabling principled control via intervention on internals. This recasts the core problem of steering from finding the right direction to finding the right geometry.

We propose CRAFT, a red-teaming alignment framework that leverages model reasoning capabilities and hidden representations to improve robustness against jailbreak attacks. Unlike prior defenses that operate primarily at the output level, CRAFT aligns large reasoning models to generate safety-aware reasoning traces by explicitly optimizing objectives defined over the hidden state space. Methodologically, CRAFT integrates contrastive representation learning with reinforcement learning to separate safe and unsafe reasoning trajectories, yielding a latent-space geometry that supports robust, reasoning-level safety alignment. Theoretically, we show that incorporating latent-textual consistency into GRPO eliminates superficially aligned policies by ruling them out as local optima. Empirically, we evaluate CRAFT on multiple safety benchmarks using two strong reasoning models, Qwen3-4B-Thinking and R1-Distill-Llama-8B, where it consistently outperforms state-of-the-art defenses such as IPO and SafeKey. Notably, CRAFT delivers an average 79.0% improvement in reasoning safety and 87.7% improvement in final-response safety over the base models, demonstrating the effectiveness of hidden-space reasoning alignment.

Large Language Models (LLMs) show strong generalization across diverse tasks, yet the internal decision-making processes behind their predictions remain opaque. In this work, we study the geometry of hidden representations in LLMs through the lens of intrinsic dimension (ID), focusing specifically on decision-making dynamics in a multiple-choice question answering (MCQA) setting. We perform a large-scale study, with 28 open-weight transformer models and estimate ID across layers using multiple estimators, while also quantifying per-layer performance on MCQA tasks. Our findings reveal a consistent ID pattern across models: early layers operate on low-dimensional manifolds, middle layers expand this space, and later layers compress it again, converging to decision-relevant representations. Together, these results suggest LLMs implicitly learn to project linguistic inputs onto structured, low-dimensional manifolds aligned with task-specific decisions, providing new geometric insights into how generalization and reasoning emerge in language models.

Topology reasoning, which unifies perception and structured reasoning, plays a vital role in understanding intersections for autonomous driving. However, its performance heavily relies on the accuracy of lane detection, particularly at connected lane endpoints. Existing methods often suffer from lane endpoints deviation, leading to incorrect topology construction. To address this issue, we propose TopoPoint, a novel framework that explicitly detects lane endpoints and jointly reasons over endpoints and lanes for robust topology reasoning. During training, we independently initialize point and lane query, and proposed Point-Lane Merge Self-Attention to enhance global context sharing through incorporating geometric distances between points and lanes as an attention mask . We further design Point-Lane Graph Convolutional Network to enable mutual feature aggregation between point and lane query. During inference, we introduce Point-Lane Geometry Matching algorithm that computes distances between detected points and lanes to refine lane endpoints, effectively mitigating endpoint deviation. Extensive experiments on the OpenLane-V2 benchmark demonstrate that TopoPoint achieves state-of-the-art performance in topology reasoning (48.8 on OLS). Additionally, we propose DET_p to evaluate endpoint detection, under which our method significantly outperforms existing approaches (52.6 v.s. 45.2 on DET_p). The code is released at https://github.com/Franpin/TopoPoint.

Vision-Language Models (VLMs) have transformed tasks requiring visual and reasoning abilities, such as image retrieval and Visual Question Answering (VQA). Despite their success, VLMs face significant challenges with tasks involving geometric reasoning, algebraic problem-solving, and counting. These limitations stem from difficulties effectively integrating multiple modalities and accurately interpreting geometry-related tasks. Various works claim that introducing a captioning pipeline before VQA tasks enhances performance. We incorporated this pipeline for tasks involving geometry, algebra, and counting. We found that captioning results are not generalizable, specifically with larger VLMs primarily trained on downstream QnA tasks showing random performance on math-related challenges. However, we present a promising alternative: task-based prompting, enriching the prompt with task-specific guidance. This approach shows promise and proves more effective than direct captioning methods for math-heavy problems.

Bird's-eye-view (BEV) is a powerful and widely adopted representation for road scenes that captures surrounding objects and their spatial locations, along with overall context in the scene. In this work, we focus on bird's eye semantic segmentation, a task that predicts pixel-wise semantic segmentation in BEV from side RGB images. This task is made possible by simulators such as Carla, which allow for cheap data collection, arbitrary camera placements, and supervision in ways otherwise not possible in the real world. There are two main challenges to this task: the view transformation from side view to bird's eye view, as well as transfer learning to unseen domains. Existing work transforms between views through fully connected layers and transfer learns via GANs. This suffers from a lack of depth reasoning and performance degradation across domains. Our novel 2-staged perception pipeline explicitly predicts pixel depths and combines them with pixel semantics in an efficient manner, allowing the model to leverage depth information to infer objects' spatial locations in the BEV. In addition, we transfer learning by abstracting high-level geometric features and predicting an intermediate representation that is common across different domains. We publish a new dataset called BEVSEG-Carla and show that our approach improves state-of-the-art by 24% mIoU and performs well when transferred to a new domain.

Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a powerful diagram parser based on deep learning and graph reasoning. Specifically, a modified instance segmentation method is proposed to extract geometric primitives, and the graph neural network (GNN) is leveraged to realize relation parsing and primitive classification incorporating geometric features and prior knowledge. All the modules are integrated into an end-to-end model called PGDPNet to perform all the sub-tasks simultaneously. In addition, we build a new large-scale geometry diagram dataset named PGDP5K with primitive level annotations. Experiments on PGDP5K and an existing dataset IMP-Geometry3K show that our model outperforms state-of-the-art methods in four sub-tasks remarkably. Our code, dataset and appendix material are available at https://github.com/mingliangzhang2018/PGDP.

We introduce Reasoning Gym (RG), a library of reasoning environments for reinforcement learning with verifiable rewards. It provides over 100 data generators and verifiers spanning multiple domains including algebra, arithmetic, computation, cognition, geometry, graph theory, logic, and various common games. Its key innovation is the ability to generate virtually infinite training data with adjustable complexity, unlike most previous reasoning datasets, which are typically fixed. This procedural generation approach allows for continuous evaluation across varying difficulty levels. Our experimental results demonstrate the efficacy of RG in both evaluating and reinforcement learning of reasoning models.

Reinforcement learning has become essential for strengthening the reasoning abilities of large language models, yet current exploration mechanisms remain fundamentally misaligned with how these models actually learn. Entropy bonuses and external semantic comparators encourage surface level variation but offer no guarantee that sampled trajectories differ in the update directions that shape optimization. We propose G2RL, a gradient guided reinforcement learning framework in which exploration is driven not by external heuristics but by the model own first order update geometry. For each response, G2RL constructs a sequence level feature from the model final layer sensitivity, obtainable at negligible cost from a standard forward pass, and measures how each trajectory would reshape the policy by comparing these features within a sampled group. Trajectories that introduce novel gradient directions receive a bounded multiplicative reward scaler, while redundant or off manifold updates are deemphasized, yielding a self referential exploration signal that is naturally aligned with PPO style stability and KL control. Across math and general reasoning benchmarks (MATH500, AMC, AIME24, AIME25, GPQA, MMLUpro) on Qwen3 base 1.7B and 4B models, G2RL consistently improves pass@1, maj@16, and pass@k over entropy based GRPO and external embedding methods. Analyzing the induced geometry, we find that G2RL expands exploration into substantially more orthogonal and often opposing gradient directions while maintaining semantic coherence, revealing that a policy own update space provides a far more faithful and effective basis for guiding exploration in large language model reinforcement learning.

Cross-view spatial reasoning remains a weak spot for vision-language models (VLMs): they often reason in language and lose the fine-grained geometry needed for the task. Thinking with images aims to address this by generating an intermediate thinking image, but recent work shows that models often ignore the visual evidence in these traces. We therefore ask how to make visual thinking matter, and what kind of visual thinking works best. We study these questions in unified multimodal models (UMMs), which natively support interleaved image-text generation. For the first question, we propose View Dropout (VDrop), a training-time intervention that hides parts of one input view from the answer span while keeping them visible to the thinking-image tokens. This encourages the model to use the thinking image when answering, instead of relying only on the input views. Once the thinking image is used for answer prediction, we study which type of visual thinking is most effective. We frame this as a learnability-informativeness tradeoff and compare three thinking-image variants: top-down, panoramic, and point-matching renderings. Trained on synthetic scenes and evaluated on five real-world out-of-domain benchmarks, panoramic visual thinking with VDrop is the only configuration that is both informative and learnable, and it achieves the best out-of-domain generalization.

Multimodal reasoning stands as a pivotal capability for large vision-language models (LVLMs). The integration with Domain-Specific Languages (DSL), offering precise visual representations, equips these models with the opportunity to execute more accurate reasoning in complex and professional domains. However, the vanilla Chain-of-Thought (CoT) prompting method faces challenges in effectively leveraging the unique strengths of visual and DSL representations, primarily due to their differing reasoning mechanisms. Additionally, it often falls short in addressing critical steps in multi-step reasoning tasks. To mitigate these challenges, we introduce the Bi-Modal Behavioral Alignment (BBA) prompting method, designed to maximize the potential of DSL in augmenting complex multi-modal reasoning tasks. This method initiates by guiding LVLMs to create separate reasoning chains for visual and DSL representations. Subsequently, it aligns these chains by addressing any inconsistencies, thus achieving a cohesive integration of behaviors from different modalities. Our experiments demonstrate that BBA substantially improves the performance of GPT-4V(ision) on geometry problem solving (28.34% to 34.22%), chess positional advantage prediction (42.08% to 46.99%) and molecular property prediction (77.47% to 83.52%).

High-quality 3D world models are pivotal for embodied intelligence and Artificial General Intelligence (AGI), underpinning applications such as AR/VR content creation and robotic navigation. Despite the established strong imaginative priors, current video foundation models lack explicit 3D grounding capabilities, thus being limited in both spatial consistency and their utility for downstream 3D reasoning tasks. In this work, we present FantasyWorld, a geometry-enhanced framework that augments frozen video foundation models with a trainable geometric branch, enabling joint modeling of video latents and an implicit 3D field in a single forward pass. Our approach introduces cross-branch supervision, where geometry cues guide video generation and video priors regularize 3D prediction, thus yielding consistent and generalizable 3D-aware video representations. Notably, the resulting latents from the geometric branch can potentially serve as versatile representations for downstream 3D tasks such as novel view synthesis and navigation, without requiring per-scene optimization or fine-tuning. Extensive experiments show that FantasyWorld effectively bridges video imagination and 3D perception, outperforming recent geometry-consistent baselines in multi-view coherence and style consistency. Ablation studies further confirm that these gains stem from the unified backbone and cross-branch information exchange.

Recent advances in large multimodal models suggest that explicit reasoning mechanisms play a critical role in improving model reliability, interpretability, and cross-modal alignment. While such reasoning-centric approaches have been proven effective in language and vision tasks, their extension to 3D remains underdeveloped. CoRe3D introduces a unified 3D understanding and generation reasoning framework that jointly operates over semantic and spatial abstractions, enabling high-level intent inferred from language to directly guide low-level 3D content formation. Central to this design is a spatially grounded reasoning representation that decomposes 3D latent space into localized regions, allowing the model to reason over geometry in a compositional and procedural manner. By tightly coupling semantic chain-of-thought inference with structured spatial reasoning, CoRe3D produces 3D outputs that exhibit strong local consistency and faithful alignment with linguistic descriptions.

Recovering the relative 6-DoF pose between two image groups underlies cross-sequence relocalization and multi-camera rig odometry. Each group carries known intra-group geometry from visual odometry or rig calibration, and pretrained multi-view backbones already fuse such geometry into visual features. Yet current models treat all views as an unstructured set, leaving cross-group reasoning as the missing piece. We introduce , which keeps the foundation model entirely frozen and adds three lightweight trainable modules to bridge the two groups: a perceiver resampler, a cross-group bridge with merged self-attention, and a multi-frame pose head. The trainable footprint totals about 32M parameters, under 6\% of the full model, and is supervised only by relative poses. Across four datasets that span indoor and outdoor simulation, real-world cross-season capture, and zero-shot sim-to-real transfer, attains state-of-the-art accuracy on both tasks, while every baseline is retrained with its full original supervision. Code is available at https://github.com/WeiYuFei0217/G2G.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

Spatial intelligence remains a persistent challenge for Multimodal Large Language Models (MLLMs), as it requires coherent spatial scene representations beyond basic object recognition. Existing methods typically build such representations through textual reasoning or 3D reconstruction. However, they often falter during multi-step reasoning, particularly when required to dynamically re-anchor evidence to the specific camera-, object-, or direction-centric reference frames demanded by complex queries. To address this, we propose OmniView-Space, a framework designed to maintain spatial consistency through multimodal egocentric evidence. Our approach consists of three core components: (1) Multi-Perspective Spatial Mapping (MPSM), which re-anchors reconstructed geometry into a query-aligned visual cognitive map and a textual spatial graph; (2) Tool-Guided Egocentric Reasoning, an interleaved policy trained to actively select the ego anchor required by the query and request the corresponding MPSM evidence; and (3) Cognitive-Map Distillation, which uses MPSM-generated trajectories and ego-frame rewards to train the model to reason with self-generated cognitive maps. Experiments on single- and multi-image spatial reasoning benchmarks show that OmniView-Space achieves state-of-the-art performance. Furthermore, the distilled model maintains this performance while reducing reliance on external geometry pipelines.

Joint estimation of surface normals and depth is essential for holistic 3D scene understanding, yet high-resolution prediction remains difficult due to the trade-off between preserving fine local detail and maintaining global consistency. To address this challenge, we propose the Ultra Resolution Geometry Transformer (URGT), which adapts the Visual Geometry Grounded Transformer (VGGT) into a unified multi-patch transformer for monocular high-resolution depth--normal estimation. A single high-resolution image is partitioned into patches that are augmented with coarse depth and normal priors from pre-trained models, and jointly processed in a single forward pass to predict refined geometric outputs. Global coherence is enforced through cross-patch attention, which enables long-range geometric reasoning and seamless propagation of information across patches within a shared backbone. To further enhance spatial robustness, we introduce a GridMix patch sampling strategy that probabilistically samples grid configurations during training, improving inter-patch consistency and generalization. Our method achieves state-of-the-art results on UnrealStereo4K, jointly improving depth and normal estimation, reducing AbsRel from 0.0582 to 0.0291, RMSE from 2.17 to 1.31, and lowering mean angular error from 23.36 degrees to 18.51 degrees, while producing sharper and more stable geometry. The proposed multi-patch framework also demonstrates strong zero-shot and cross-domain generalization and scales effectively to very high resolutions, offering an efficient and extensible solution for high-quality geometry refinement.

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic and spherical spaces show promise for hierarchical and cyclical patterns, respectively, they require committing to a single geometry a priori, reducing flexibility when data exhibits mixed geometric properties. We introduce the Curvature-Adaptive Transformer (CAT), a novel architecture that dynamically learns per-token routing across three geometric attention branches through a lightweight, differentiable gating mechanism. Unlike fixed-geometry approaches, CAT enables adaptive geometric specialization, routing tokens to the appropriate curvature based on their local relational structure. The routing network provides interpretable curvature preferences while each branch employs geometry-specific operations optimized for its respective manifold. On knowledge graph completion benchmarks (FB15k-237, WN18RR), CAT achieves approximately 10% improvements in MRR and Hits@10 over fixed-geometry baselines with minimal overhead (5% parameter increase, comparable inference time). These results demonstrate that learned geometric adaptation outperforms any single fixed geometry for complex relational reasoning, establishing CAT as a scalable and interpretable foundation for mixture-of-geometry architectures across language, vision, and multimodal domains.

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

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

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains underexplored. In this paper, we address this gap by formalizing the Program-to-Geometry task, which challenges models to translate programmatic drawing code into accurate and abstract geometric reasoning. To evaluate this capability, we present GeoGramBench, a benchmark of 500 carefully refined problems organized by a tailored three-level taxonomy that considers geometric complexity rather than traditional mathematical reasoning complexity. Our comprehensive evaluation of 17 frontier LLMs reveals consistent and pronounced deficiencies: even the most advanced models achieve less than 50% accuracy at the highest abstraction level. These results highlight the unique challenges posed by program-driven spatial reasoning and establish GeoGramBench as a valuable resource for advancing research in symbolic-to-spatial geometric reasoning. Project page: https://github.com/LiAuto-DSR/GeoGramBench.

Abstract visual reasoning (AVR) encompasses a suite of tasks whose solving requires the ability to discover common concepts underlying the set of pictures through an analogy-making process, similarly to human IQ tests. Bongard Problems (BPs), proposed in 1968, constitute a fundamental challenge in this domain mainly due to their requirement to combine visual reasoning and verbal description. This work poses a question whether multimodal large language models (MLLMs) inherently designed to combine vision and language are capable of tackling BPs. To this end, we propose a set of diverse MLLM-suited strategies to tackle BPs and examine four popular proprietary MLLMs: GPT-4o, GPT-4 Turbo, Gemini 1.5 Pro, and Claude 3.5 Sonnet, and four open models: InternVL2-8B, LLaVa-1.6 Mistral-7B, Phi-3.5-Vision, and Pixtral 12B. The above MLLMs are compared on three BP datasets: a set of original BP instances relying on synthetic, geometry-based images and two recent datasets based on real-world images, i.e., Bongard-HOI and Bongard-OpenWorld. The experiments reveal significant limitations of MLLMs in solving BPs. In particular, the models struggle to solve the classical set of synthetic BPs, despite their visual simplicity. Though their performance ameliorates on real-world concepts expressed in Bongard-HOI and Bongard-OpenWorld, the models still have difficulty in utilizing new information to improve their predictions, as well as utilizing a dialog context window effectively. To capture the reasons of performance discrepancy between synthetic and real-world AVR domains, we propose Bongard-RWR, a new BP dataset consisting of real-world images that translates concepts from hand-crafted synthetic BPs to real-world concepts. The MLLMs' results on Bongard-RWR suggest that their poor performance on classical BPs is not due to domain specificity but rather reflects their general AVR limitations.

In this work, we aim to improve the 3D reasoning ability of Transformers in multi-view 3D human pose estimation. Recent works have focused on end-to-end learning-based transformer designs, which struggle to resolve geometric information accurately, particularly during occlusion. Instead, we propose a novel hybrid model, MVGFormer, which has a series of geometric and appearance modules organized in an iterative manner. The geometry modules are learning-free and handle all viewpoint-dependent 3D tasks geometrically which notably improves the model's generalization ability. The appearance modules are learnable and are dedicated to estimating 2D poses from image signals end-to-end which enables them to achieve accurate estimates even when occlusion occurs, leading to a model that is both accurate and generalizable to new cameras and geometries. We evaluate our approach for both in-domain and out-of-domain settings, where our model consistently outperforms state-of-the-art methods, and especially does so by a significant margin in the out-of-domain setting. We will release the code and models: https://github.com/XunshanMan/MVGFormer.

Human perception for effective object tracking in a 2D video stream arises from the implicit use of prior 3D knowledge combined with semantic reasoning. In contrast, most generic object tracking (GOT) methods primarily rely on 2D features of the target and its surroundings while neglecting 3D geometric cues, which makes them susceptible to partial occlusion, distractors, and variations in geometry and appearance. To address this limitation, we introduce GOT-Edit, an online cross-modality model editing approach that integrates geometry-aware cues into a generic object tracker from a 2D video stream. Our approach leverages features from a pre-trained Visual Geometry Grounded Transformer to enable geometric cue inference from only a few 2D images. To tackle the challenge of seamlessly combining geometry and semantics, GOT-Edit performs online model editing with null-space constrained updates that incorporate geometric information while preserving semantic discrimination, yielding consistently better performance across diverse scenarios. Extensive experiments on multiple GOT benchmarks demonstrate that GOT-Edit achieves superior robustness and accuracy, particularly under occlusion and clutter, establishing a new paradigm for combining 2D semantics with 3D geometric reasoning for generic object tracking.

Vision-Language-Action (VLA) models have emerged as a powerful end-to-end paradigm for robotic manipulation by mapping language instructions and 2D visual inputs directly to actions. However, these models lack an explicit, scene-level 3D representation, limiting their ability to reason over spatial layouts and geometric constraints. While recent efforts incorporate explicit 3D cues, such as depth maps or point clouds, to improve geometric awareness, they primarily capture low-level structures and lack high-level semantic grounding in 3D space. In human cognition, interaction with the physical world relies on a 3D semantic cognitive map - an internal mental model that integrates spatial layouts with semantic context to enable persistent, viewpoint-invariant reasoning. In light of this, we present VistaVLA, a novel two-stage framework that constructs a geometry- and semantics-aware 3D cognitive representation from 3D Gaussian primitives and grounds it as compact context tokens for VLA policy learning. Specifically, VistaVLA lifts multi-view vision-language features into 3D Gaussian primitives, forming geometry-anchored semantic tokens that align view-consistent spatial grounding with 2D visual feature spaces. To make this 3D representation computationally tractable for effective VLA control, we introduce Merge-then-Query (MtQ), a token summarization mechanism. MtQ compresses dense Gaussian primitives into a highly compact set of spatially informative tokens, achieving a 99% token reduction while preserving action-relevant 3D layouts and semantic context. Extensive evaluations in both simulated and real-world environments demonstrate the effectiveness of VistaVLA. Notably, in real-world scenarios, VistaVLA improves success rates by 22.8% across seven real-world tasks and by 30.0% over the VLA-Adapter baseline on challenging out-of-distribution tasks.

Plane Geometry Diagram Synthesis has been a crucial task in computer graphics, with applications ranging from educational tools to AI-driven mathematical reasoning. Traditionally, we rely on manual tools (e.g., Matplotlib and GeoGebra) to generate precise diagrams, but this usually requires huge, complicated calculations. Recently, researchers start to work on model-based methods (e.g., Stable Diffusion and GPT5) to automatically generate diagrams, saving operational cost but usually suffering from limited realism and insufficient accuracy. In this paper, we propose a novel framework GeoSDF, to automatically generate diagrams efficiently and accurately with Signed Distance Field (SDF). Specifically, we first represent geometric elements (e.g., points, segments, and circles) in the SDF, then construct a series of constraint functions to represent geometric relationships. Next, we optimize those constructed constraint functions to get an optimized field of both elements and constraints. Finally, by rendering the optimized field, we can obtain the synthesized diagram. In our GeoSDF, we define a symbolic language to represent geometric elements and constraints, and our synthesized geometry diagrams can be self-verified in the SDF, ensuring both mathematical accuracy and visual plausibility. In experiments, through both qualitative and quantitative analysis, GeoSDF synthesized both normal high-school level and IMO-level geometry diagrams. We achieve 88.67\% synthesis accuracy by human evaluation in the IMO problem set. Furthermore, we obtain a very high accuracy of solving geometry problems (over 95\% while the current SOTA accuracy is around 75%) by leveraging our self-verification property. All of these demonstrate the advantage of GeoSDF, paving the way for more sophisticated, accurate, and flexible generation of geometric diagrams for a wide array of applications.

Chain-of-Thought (CoT) reasoning has become a powerful driver of trajectory prediction in VLA-based autonomous driving, yet its autoregressive nature imposes a latency cost that is prohibitive for real-time deployment. Latent CoT methods attempt to close this gap by compressing reasoning into continuous hidden states, but consistently fall short of their explicit counterparts. We suggest that this is due to purely linguistic latent representations compressing a symbolic abstraction of the world, rather than the causal dynamics that actually govern driving. Thus, we present OneVL (One-step latent reasoning and planning with Vision-Language explanations), a unified VLA and World Model framework that routes reasoning through compact latent tokens supervised by dual auxiliary decoders. Alongside a language decoder that reconstructs text CoT, we introduce a visual world model decoder that predicts future-frame tokens, forcing the latent space to internalize the causal dynamics of road geometry, agent motion, and environmental change. A three-stage training pipeline progressively aligns these latents with trajectory, language, and visual objectives, ensuring stable joint optimization. At inference, the auxiliary decoders are discarded and all latent tokens are prefilled in a single parallel pass, matching the speed of answer-only prediction. Across four benchmarks, OneVL becomes the first latent CoT method to surpass explicit CoT, delivering state-of-the-art accuracy at answer-only latency, and providing direct evidence that tighter compression, when guided in both language and world-model supervision, produces more generalizable representations than verbose token-by-token reasoning. Project Page: https://xiaomi-embodied-intelligence.github.io/OneVL

Current evaluations of spatial intelligence can be systematically invalid under modern vision-language model (VLM) settings. First, many benchmarks derive question-answer (QA) pairs from point-cloud-based 3D annotations originally curated for traditional 3D perception. When such annotations are treated as ground truth for video-based evaluation, reconstruction and annotation artifacts can miss objects that are clearly visible in the video, mislabel object identities, or corrupt geometry-dependent answers (e.g., size), yielding incorrect or ambiguous QA pairs. Second, evaluations often assume full-scene access, while many VLMs operate on sparsely sampled frames (e.g., 16-64), making many questions effectively unanswerable under the actual model inputs. We improve evaluation validity by introducing ReVSI, a benchmark and protocol that ensures each QA pair is answerable and correct under the model's actual inputs. To this end, we re-annotate objects and geometry across 381 scenes from 5 datasets to improve data quality, and regenerate all QA pairs with rigorous bias mitigation and human verification using professional 3D annotation tools. We further enhance evaluation controllability by providing variants across multiple frame budgets (16/32/64/all) and fine-grained object visibility metadata, enabling controlled diagnostic analyses. Evaluations of general and domain-specific VLMs on ReVSI reveal systematic failure modes that are obscured by prior benchmarks, yielding a more reliable and diagnostic assessment of spatial intelligence.

Most existing 3D referring expression segmentation (3DRES) methods rely on dense, high-quality point clouds, while real-world agents such as robots and mobile phones operate with only a few sparse RGB views and strict latency constraints. We introduce Multi-view 3D Referring Expression Segmentation (MV-3DRES), where the model must recover scene structure and segment the referred object directly from sparse multi-view images. Traditional two-stage pipelines, which first reconstruct a point cloud and then perform segmentation, often yield low-quality geometry, produce coarse or degraded target regions, and run slowly. We propose the Multimodal Visual Geometry Grounded Transformer (MVGGT), an efficient end-to-end framework that integrates language information into sparse-view geometric reasoning through a dual-branch design. Training in this setting exposes a critical optimization barrier, termed Foreground Gradient Dilution (FGD), where sparse 3D signals lead to weak supervision. To resolve this, we introduce Per-view No-target Suppression Optimization (PVSO), which provides stronger and more balanced gradients across views, enabling stable and efficient learning. To support consistent evaluation, we build MVRefer, a benchmark that defines standardized settings and metrics for MV-3DRES. Experiments show that MVGGT establishes the first strong baseline and achieves both high accuracy and fast inference, outperforming existing alternatives. Code and models are publicly available at https://mvggt.github.io.

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.

Recently, world-action models (WAM) have emerged to bridge vision-language-action (VLA) models and world models, unifying their reasoning and instruction-following capabilities and spatio-temporal world modeling. However, existing WAM approaches often focus on modeling 2D appearance or latent representations, with limited geometric grounding-an essential element for embodied systems operating in the physical world. We present DriveDreamer-Policy, a unified driving world-action model that integrates depth generation, future video generation, and motion planning within a single modular architecture. The model employs a large language model to process language instructions, multi-view images, and actions, followed by three lightweight generators that produce depth, future video, and actions. By learning a geometry-aware world representation and using it to guide both future prediction and planning within a unified framework, the proposed model produces more coherent imagined futures and more informed driving actions, while maintaining modularity and controllable latency. Experiments on the Navsim v1 and v2 benchmarks demonstrate that DriveDreamer-Policy achieves strong performance on both closed-loop planning and world generation tasks. In particular, our model reaches 89.2 PDMS on Navsim v1 and 88.7 EPDMS on Navsim v2, outperforming existing world-model-based approaches while producing higher-quality future video and depth predictions. Ablation studies further show that explicit depth learning provides complementary benefits to video imagination and improves planning robustness.

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

We present PhysInOne, a large-scale synthetic dataset addressing the critical scarcity of physically-grounded training data for AI systems. Unlike existing datasets limited to merely hundreds or thousands of examples, PhysInOne provides 2 million videos across 153,810 dynamic 3D scenes, covering 71 basic physical phenomena in mechanics, optics, fluid dynamics, and magnetism. Distinct from previous works, our scenes feature multiobject interactions against complex backgrounds, with comprehensive ground-truth annotations including 3D geometry, semantics, dynamic motion, physical properties, and text descriptions. We demonstrate PhysInOne's efficacy across four emerging applications: physics-aware video generation, long-/short-term future frame prediction, physical property estimation, and motion transfer. Experiments show that fine-tuning foundation models on PhysInOne significantly enhances physical plausibility, while also exposing critical gaps in modeling complex physical dynamics and estimating intrinsic properties. As the largest dataset of its kind, orders of magnitude beyond prior works, PhysInOne establishes a new benchmark for advancing physics-grounded world models in generation, simulation, and embodied AI.

The reliability of Large Language Models (LLMs) in high-stakes domains such as healthcare, law, and scientific discovery is often compromised by hallucinations. These failures typically stem from two sources: data-driven hallucinations and reasoning-driven hallucinations. However, existing detection methods usually address only one source and rely on task-specific heuristics, limiting their generalization to complex scenarios. To overcome these limitations, we introduce the Hallucination Risk Bound, a unified theoretical framework that formally decomposes hallucination risk into data-driven and reasoning-driven components, linked respectively to training-time mismatches and inference-time instabilities. This provides a principled foundation for analyzing how hallucinations emerge and evolve. Building on this foundation, we introduce HalluGuard, an NTK-based score that leverages the induced geometry and captured representations of the NTK to jointly identify data-driven and reasoning-driven hallucinations. We evaluate HalluGuard on 10 diverse benchmarks, 11 competitive baselines, and 9 popular LLM backbones, consistently achieving state-of-the-art performance in detecting diverse forms of LLM hallucinations.

Recent advancements in vision-language-action (VLA) models have shown promise in robotic manipulation, yet they continue to struggle with long-horizon, multi-step tasks. Existing methods lack internal reasoning mechanisms that can identify task-relevant interaction cues or track progress within a subtask, leading to critical execution errors such as repeated actions, missed steps, and premature termination. To address these challenges, we introduce PALM, a VLA framework that structures policy learning around interaction-centric affordance reasoning and subtask progress cues. PALM distills complementary affordance representations that capture object relevance, contact geometry, spatial placements, and motion dynamics, and serve as task-relevant anchors for visuomotor control. To further stabilize long-horizon execution, PALM predicts continuous within-subtask progress, enabling seamless subtask transitions. Across extensive simulation and real-world experiments, PALM consistently outperforms baselines, achieving a 91.8% success rate on LIBERO-LONG, a 12.5% improvement in average length on CALVIN ABC->D, and a 2x improvement over real-world baselines across three long-horizon generalization settings.

The rapid development of Large Multimodal Models (LMMs) has led to remarkable progress in 2D visual understanding; however, extending these capabilities to 3D scene understanding remains a significant challenge. Existing approaches predominantly rely on text-only supervision, which fails to provide the geometric constraints required for learning robust 3D spatial representations. In this paper, we introduce Reg3D, a novel Reconstructive Geometry Instruction Tuning framework that addresses this limitation by incorporating geometry-aware supervision directly into the training process. Our key insight is that effective 3D understanding necessitates reconstructing underlying geometric structures rather than merely describing them. Unlike existing methods that inject 3D information solely at the input level, Reg3D adopts a dual-supervision paradigm that leverages 3D geometric information both as input and as explicit learning targets. Specifically, we design complementary object-level and frame-level reconstruction tasks within a dual-encoder architecture, enforcing geometric consistency to encourage the development of spatial reasoning capabilities. Extensive experiments on ScanQA, Scan2Cap, ScanRefer, and SQA3D demonstrate that Reg3D delivers substantial performance improvements, establishing a new training paradigm for spatially aware multimodal models.

Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework designed to generate formally verifiable geometric solutions from textual descriptions and visual diagrams. Geoint-R1 uniquely integrates auxiliary elements construction, formal reasoning represented via Lean4, and interactive visualization. To systematically evaluate and advance formal geometric reasoning, we propose the Geoint benchmark, comprising 1,885 rigorously annotated geometry problems across diverse topics such as plane, spatial, and solid geometry. Each problem includes structured textual annotations, precise Lean4 code for auxiliary constructions, and detailed solution steps verified by experts. Extensive experiments demonstrate that Geoint-R1 significantly surpasses existing multimodal and math-specific reasoning models, particularly on challenging problems requiring explicit auxiliary element constructions.

Benchmarking spatial reasoning in multimodal large language models (MLLMs) has attracted growing interest in computer vision due to its importance for embodied AI and other agentic systems that require precise interaction with the physical world. However, spatial reasoning on Earth imagery has lagged behind, as it uniquely involves grounding objects in georeferenced images and quantitatively reasoning about distances, directions, and topological relations using both visual cues and vector geometry coordinates (e.g., 2D bounding boxes, polylines, and polygons). Existing benchmarks for Earth imagery primarily focus on 2D spatial grounding, image captioning, and coarse spatial relations (e.g., simple directional or proximity cues). They lack support for quantitative direction and distance reasoning, systematic topological relations, and complex object geometries beyond bounding boxes. To fill this gap, we propose EarthSpatialBench, a comprehensive benchmark for evaluating spatial reasoning in MLLMs on Earth imagery. The benchmark contains over 325K question-answer pairs spanning: (1) qualitative and quantitative reasoning about spatial distance and direction; (2) systematic topological relations; (3) single-object queries, object-pair queries, and compositional aggregate group queries; and (4) object references expressed via textual descriptions, visual overlays, and explicit geometry coordinates, including 2D bounding boxes, polylines, and polygons. We conducted extensive experiments on both open-source and proprietary models to identify limitations in the spatial reasoning of MLLMs.

Modern monocular 3D reconstruction methods and vision-language models (VLMs) demonstrate impressive results on standard benchmarks, yet recent works cast doubt on their true understanding of geometric properties. We introduce GOQ, a comprehensive benchmark specifically designed to evaluate the geometric reasoning capabilities of vision and vision-language foundation models. GIQ comprises synthetic and real-world images and corresponding 3D meshes of diverse polyhedra covering varying levels of complexity and symmetry, from Platonic, Archimedean, Johnson, and Catalan solids to stellations and compound shapes. Through systematic experiments involving monocular 3D reconstruction, 3D symmetry detection, mental rotation tests, and zero-shot shape classification tasks, we reveal significant shortcomings in current models. State-of-the-art reconstruction algorithms trained on extensive 3D datasets struggle to reconstruct even basic geometric Platonic solids accurately. Next, although foundation models may be shown via linear and non-linear probing to capture specific 3D symmetry elements, they falter significantly in tasks requiring detailed geometric differentiation, such as mental rotation. Moreover, advanced vision-language assistants such as ChatGPT, Gemini and Claud exhibit remarkably low accuracy in interpreting basic shape properties such as face geometry, convexity, and compound structures of complex polyhedra. GIQ is publicly available at toomanymatts.github.io/giq-benchmark/, providing a structured platform to benchmark critical gaps in geometric intelligence and facilitate future progress in robust, geometry-aware representation learning.

Chain-of-Thought (CoT) reasoning excels in language models but struggles in vision-language models due to premature visual-to-text conversion that discards continuous information such as geometry and spatial layout. While recent methods enhance CoT through static enumeration or attention-based selection, they remain passive, i.e., processing pre-computed inputs rather than actively seeking task-relevant details. Inspired by human active perception, we introduce ViThinker, a framework that enables vision-language models to autonomously generate decision (query) tokens triggering the synthesis of expert-aligned visual features on demand. ViThinker internalizes vision-expert capabilities during training, performing generative mental simulation during inference without external tool calls. Through a two-stage curriculum: first distilling frozen experts into model parameters, then learning task-driven querying via sparsity penalties, i.e., ViThinker discovers minimal sufficient perception for each reasoning step. Evaluations across vision-centric benchmarks demonstrate consistent improvements, validating that active query generation outperforms passive approaches in both perceptual grounding and reasoning accuracy.

Language-driven dexterous grasp generation requires the models to understand task semantics, 3D geometry, and complex hand-object interactions. While vision-language models have been applied to this problem, existing approaches directly map observations to grasp parameters without intermediate reasoning about physical interactions. We present DextER, Dexterous Grasp Generation with Embodied Reasoning, which introduces contact-based embodied reasoning for multi-finger manipulation. Our key insight is that predicting which hand links contact where on the object surface provides an embodiment-aware intermediate representation bridging task semantics with physical constraints. DextER autoregressively generates embodied contact tokens specifying which finger links contact where on the object surface, followed by grasp tokens encoding the hand configuration. On DexGYS, DextER achieves 67.14% success rate, outperforming state-of-the-art by 3.83%p with 96.4% improvement in intention alignment. We also demonstrate steerable generation through partial contact specification, providing fine-grained control over grasp synthesis.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

Existing methodologies in open vocabulary 3D semantic segmentation primarily concentrate on establishing a unified feature space encompassing 3D, 2D, and textual modalities. Nevertheless, traditional techniques such as global feature alignment or vision-language model distillation tend to impose only approximate correspondence, struggling notably with delineating fine-grained segmentation boundaries. To address this gap, we propose a more meticulous mask-level alignment between 3D features and the 2D-text embedding space through a cross-modal mask reasoning framework, XMask3D. In our approach, we developed a mask generator based on the denoising UNet from a pre-trained diffusion model, leveraging its capability for precise textual control over dense pixel representations and enhancing the open-world adaptability of the generated masks. We further integrate 3D global features as implicit conditions into the pre-trained 2D denoising UNet, enabling the generation of segmentation masks with additional 3D geometry awareness. Subsequently, the generated 2D masks are employed to align mask-level 3D representations with the vision-language feature space, thereby augmenting the open vocabulary capability of 3D geometry embeddings. Finally, we fuse complementary 2D and 3D mask features, resulting in competitive performance across multiple benchmarks for 3D open vocabulary semantic segmentation. Code is available at https://github.com/wangzy22/XMask3D.

Humans have the ability to reason about geometric patterns in images and scenes from a young age. However, developing large multimodal models (LMMs) capable of similar reasoning remains a challenge, highlighting the need for robust evaluation methods to assess these capabilities. We introduce \Turtle, a benchmark designed to evaluate LMMs' capacity to interpret geometric patterns -- given visual examples, textual instructions, or both -- and generate precise code outputs. Inspired by turtle geometry, a notion used to teach children foundational coding and geometric concepts, TurtleBench features tasks with patterned shapes that have underlying algorithmic logic. Our evaluation reveals that leading LMMs struggle significantly with these tasks, with GPT-4o achieving only 19\% accuracy on the simplest tasks and few-shot prompting only marginally improves their performance (<2%). \Turtle highlights the gap between human and AI performance in intuitive and visual geometrical understanding, setting the stage for future research in this area. \Turtle stands as one of the few benchmarks to evaluate the integration of visual understanding and code generation capabilities in LMMs, setting the stage for future research. Code and Dataset for this paper is provided here: https://github.com/sinaris76/TurtleBench{https://github.com/sinaris76/TurtleBench}

Rendering photo-realistic novel-view images of complex scenes has been a long-standing challenge in computer graphics. In recent years, great research progress has been made on enhancing rendering quality and accelerating rendering speed in the realm of view synthesis. However, when rendering complex dynamic scenes with sparse views, the rendering quality remains limited due to occlusion problems. Besides, for rendering high-resolution images on dynamic scenes, the rendering speed is still far from real-time. In this work, we propose a generalizable view synthesis method that can render high-resolution novel-view images of complex static and dynamic scenes in real-time from sparse views. To address the occlusion problems arising from the sparsity of input views and the complexity of captured scenes, we introduce an explicit 3D visibility reasoning approach that can efficiently estimate the visibility of sampled 3D points to the input views. The proposed visibility reasoning approach is fully differentiable and can gracefully fit inside the volume rendering pipeline, allowing us to train our networks with only multi-view images as supervision while refining geometry and texture simultaneously. Besides, each module in our pipeline is carefully designed to bypass the time-consuming MLP querying process and enhance the rendering quality of high-resolution images, enabling us to render high-resolution novel-view images in real-time.Experimental results show that our method outperforms previous view synthesis methods in both rendering quality and speed, particularly when dealing with complex dynamic scenes with sparse views.