Geometry problem solving poses distinct challenges in artificial intelligence. Existing approaches typically fall into two paradigms: symbolic methods, which exhibit limited adaptability, and neural methods, which are prone to hallucinations. Recent neuro-symbolic hybrids predominantly rely on a unidirectional pipeline where neural outputs are fed into solvers without feedback, making system brittle to early-stage errors. To break this unidirectional bottleneck, we propose BiNSGPS, a framework that establishes Bidirectional Neuro-Symbolic Interaction (BiNS) between a MLLM Adviser and a Symbolic Solver. MLLM Adviser actively incorporates feedback from the symbolic solver to dynamically rectify inconsistent formal representations or propose auxiliary hypotheses, resolving symbolic conflicts and facilitating complex deductions. Experiments show that BiNSGPS achieves state-of-the-art performance, reaching 90.5% completion accuracy on Geometry3K and 90.1% on PGPS9K, while maintaining 96% step-wise logical coherence to balance capability with mathematical rigor.

Multimodal large language models (MLLMs) have achieved strong performance on perception-oriented tasks, yet their ability to perform mathematical spatial reasoning, defined as the capacity to parse and manipulate two- and three-dimensional relations, remains unclear. While humans easily master textbook-style spatial problems, current MLLMs exhibit substantially higher error rates, exposing a fundamental weakness in spatial comprehension. To investigate this gap, we present MathSpatial, the first large-scale and systematic dataset resource dedicated to mathematical spatial reasoning in MLLMs. MathSpatial provides two complementary subsets: MathSpatial-Bench (2,000 problems) for evaluating spatial reasoning isolated from perceptual noise, and MathSpatial-Corpus (8,000 problems) equipped with structured reasoning traces for training. Benchmarking 20+ MLLMs reveals a severe deficit: non-reasoning models largely languish below 60% accuracy, and even the strongest reasoning models fall ~16 percentage points behind human performance (96.3%). Crucially, we demonstrate that fine-tuning on MathSpatial-Corpus yields consistent performance gains across model families. MathSpatial provides a vital resource for diagnosing and advancing spatial reasoning in MLLMs. The dataset and related resources are available at https://github.com/shuolucs/MathSpatial.

Large vision-language models (LVLMs) have made rapid advancements; however, existing benchmarks for evaluating their instruction-following abilities focus on purely textual constraints, e.g., format constraints and role-playing, which assess only language-level adherence and are not related to vision. To bridge this gap, we introduce VC-IF, a benchmark that involves visual constraints connecting instructions to explicit operations over image content, thereby directly probing visual spatial understanding and compositional compliance. VC-IF defines atomic constraints, systematically combining mixed settings, scaling from single- to multi-constraint scenarios, and single- and multi-turn scenarios. We evaluate 16 popular LVLMs and find that models performing well under text-only constraints may struggle when faced with visual constraints, highlighting significant gaps in their capabilities. Further, we conduct scaling analyses across varying numbers of constraints and dialogue turns, revealing performance trends as constraint complexity increases along different dimensions. Finally, we synthesize a large training dataset and propose VC-PO, a reinforcement learning strategy that uses a hybrid verifier mechanism to compute reward signals for multiple constraints. Applying VC-PO to Qwen3-VL-8B-Instruct improves its overall VC-IF score from 43.74 to 55.18 (+11.44). The VC-PO-trained model remains stable as the number of turns and constraints increases. Our data and code are available at VC-IF.

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. We propose a training paradigm combining Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards, which effectively enforces syntactic correctness and geometric consistency. 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.

Large Language Models (LLMs) have recently achieved remarkable progress on complex reasoning tasks by leveraging extended Chain-of-Thought (CoT) techniques. These reasoning processes can be roughly categorized into System-1 (fast and intuitive) and System-2 (slow and deliberate) paradigms. However, excessive reliance on lengthy System-2-style reasoning during inference can produce extremely long outputs, thereby reducing efficiency. In this work, we propose Thinking Length Data Re-weighting (TLDR), that does not rely on sophisticated data annotations or interpolation between multiple models. We continuously balance the weights between the model’s System-1 and System-2 data to eliminate redundant reasoning processes while preserving the model’s reasoning capability. We validate our method across multiple base models, including Deepseek-R1-Distilled Qwen models, as well as on a diverse benchmarks with varying difficulty levels. Our method significantly reduces the number of output tokens by nearly 40% while maintaining the accuracy of the reasoning.

Large vision language models (LVLMs) have improved the document understanding capabilities remarkably, enabling the handling of complex document elements, longer contexts, and a wider range of tasks. However, existing document understanding benchmarks have been limited to handling only a small number of pages and fail to provide a comprehensive analysis of layout elements locating. In this paper, we first define three primary task categories: Long Document Understanding, numerical Reasoning, and cross-element Locating, and then propose a comprehensive benchmark—LongDocURL—integrating above three primary tasks and comprising 20 sub-tasks categorized based on different primary tasks and answer evidences. Furthermore, we develop a semi-automated construction pipeline and collect 2,325 high-quality question-answering pairs, covering more than 33,000 pages of documents, significantly outperforming existing benchmarks. Subsequently, we conduct comprehensive evaluation experiments on both open-source and closed- source models across 26 different configurations, revealing critical performance gaps in this field. The code and data: https://github.com/dengc2023/LongDocURL.