The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide foundation models and sophisticated agentic systems pushing the boundaries of formal mathematical reasoning to approach the natural language capability of LLMs. However, little attention has been given to the formal physics reasoning, which also heavily relies on similar problem-solving and theorem-proving frameworks. To solve this problem, this paper presents, to the best of our knowledge, the first approach to enhance formal theorem proving in the physics domain. We compose a dedicated dataset PhysLeanData for the task. It is composed of theorems sampled from PhysLean and data generated by a conjecture-based formal data generation pipeline. In the training pipeline, we leverage DeepSeek-Prover-V2-7B, a strong open-source mathematical theorem prover, and apply Reinforcement Learning with Verifiable Rewards (RLVR) to train our model PhysProver. Comprehensive experiments demonstrate that, using only about 5.5K training samples, PhysProver achieves an overall 2.4% improvement in multiple sub-domains. Furthermore, after formal physics training, we observe 1.3% gains on the MiniF2F-Test benchmark, which indicates non-trivial generalization beyond physics domains and enhancement for formal math capability as well. The results highlight the effectiveness and efficiency of our approach, which provides a paradigm for extending formal provers outside mathematical domains. To foster further research, we will release both our dataset and model to the community.

Multimodal Large Language Models (MLLMs) have shown significant promise in various applications, leading to broad interest from researchers and practitioners alike. However, a comprehensive evaluation of their long-context capabilities remains underexplored. To address these gaps, we introduce the MultiModal Needle-in-a-haystack (MMNeedle) benchmark, specifically designed to assess the long-context capabilities of MLLMs. Besides multi-image input, we employ image stitching to further increase the input context length, and develop a protocol to automatically generate labels for sub-image level retrieval. Essentially, MMNeedle evaluates MLLMs by stress-testing their capability to locate a target sub-image (needle) within a set of images (haystack) based on textual instructions and descriptions of image contents. This setup necessitates an advanced understanding of extensive visual contexts and effective information retrieval within long-context image inputs. With this benchmark, we evaluate state-of-the-art MLLMs, encompassing both API-based and open-source models. The findings reveal that GPT-4o consistently surpasses other models in long-context scenarios, but suffers from hallucination problems in negative samples, i.e., when needles are not in the haystacks. Our comprehensive long-context evaluation of MLLMs also sheds lights on the considerable performance gap between API-based and open-source models. All the code, data, and instructions required to reproduce the main results are available at https://github.com/Wang-ML-Lab/multimodal-needle-in-a-haystack.