GeometryZero: Improving Geometry Solving for LLM with Group Contrastive Policy Optimization

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.

VidCRAFT3: Camera, Object, and Lighting Control for Image-to-Video Generation

Recent image-to-video generation methods have demonstrated success in enabling control over one or two visual elements, such as camera trajectory or object motion. However, these methods are unable to offer control over multiple visual elements due to limitations in data and network efficacy. In this paper, we introduce VidCRAFT3, a novel framework for precise image-to-video generation that enables control over camera motion, object motion, and lighting direction simultaneously. To better decouple control over each visual element, we propose the Spatial Triple-Attention Transformer, which integrates lighting direction, text, and image in a symmetric way. Since most real-world video datasets lack lighting annotations, we construct a high-quality synthetic video dataset, the VideoLightingDirection (VLD) dataset. This dataset includes lighting direction annotations and objects of diverse appearance, enabling VidCRAFT3 to effectively handle strong light transmission and reflection effects. Additionally, we propose a three-stage training strategy that eliminates the need for training data annotated with multiple visual elements (camera motion, object motion, and lighting direction) simultaneously. Extensive experiments on benchmark datasets demonstrate the efficacy of VidCRAFT3 in producing high-quality video content, surpassing existing state-of-the-art methods in terms of control granularity and visual coherence. All code and data will be publicly available.