Solving Inequality Proofs with Large Language Models

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Cartridges: Lightweight and general-purpose long context representations via self-study

Large language models are often used to answer queries grounded in large text corpora (e.g. codebases, legal documents, or chat histories) by placing the entire corpus in the context window and leveraging in-context learning (ICL). Although current models support contexts of 100K-1M tokens, this setup is costly to serve because the memory consumption of the KV cache scales with input length. We explore an alternative: training a smaller KV cache offline on each corpus. At inference time, we load this trained KV cache, which we call a Cartridge, and decode a response. Critically, the cost of training a Cartridge can be amortized across all the queries referencing the same corpus. However, we find that the naive approach of training the Cartridge with next-token prediction on the corpus is not competitive with ICL. Instead, we propose self-study, a training recipe in which we generate synthetic conversations about the corpus and train the Cartridge with a context-distillation objective. We find that Cartridges trained with self-study replicate the functionality of ICL, while being significantly cheaper to serve. On challenging long-context benchmarks, Cartridges trained with self-study match ICL performance while using 38.6x less memory and enabling 26.4x higher throughput. Self-study also extends the model's effective context length (e.g. from 128k to 484k tokens on MTOB) and surprisingly, leads to Cartridges that can be composed at inference time without retraining.

Inference-time Scaling of Diffusion Models through Classical Search

Classical search algorithms have long underpinned modern artificial intelligence. In this work, we tackle the challenge of inference-time control in diffusion models -- adapting generated outputs to meet diverse test-time objectives -- using principles from classical search. We propose a general framework that orchestrates local and global search to efficiently navigate the generative space. It employs a theoretically grounded local search via annealed Langevin MCMC and performs compute-efficient global exploration using breadth-first and depth-first tree search. We evaluate our approach on a range of challenging domains, including planning, offline reinforcement learning, and image generation. Across all tasks, we observe significant gains in both performance and efficiency. These results show that classical search provides a principled and practical foundation for inference-time scaling in diffusion models. Project page at diffusion-inference-scaling.github.io.

A Snapshot of Influence: A Local Data Attribution Framework for Online Reinforcement Learning

Online reinforcement learning (RL) excels in complex, safety-critical domains, yet it faces challenges such as sample inefficiency, training instability, and a lack of interpretability. Data attribution offers a principled way to trace model behavior back to individual training samples. However, in online RL, each training sample not only drives policy updates but also influences future data collection, violating the fixed dataset assumption in existing attribution methods. In this paper, we initiate the study of data attribution for online RL, focusing on the widely used Proximal Policy Optimization (PPO) algorithm. We start by establishing a local attribution framework, interpreting model checkpoints with respect to the records in the recent training buffer. We design two target functions, capturing agent action and cumulative return respectively, and measure each record's contribution through gradient similarity between its training loss and these targets. We demonstrate the power of this framework through three concrete applications: diagnosis of learning, temporal analysis of behavior formation, and targeted intervention during training. Leveraging this framework, we further propose an algorithm, iterative influence-based filtering (IIF), for online RL training that iteratively performs experience filtering to refine policy updates. Across standard RL benchmarks (classic control, navigation, locomotion) to RLHF for large language models, IIF reduces sample complexity, speeds up training, and achieves higher returns. Overall, these results advance interpretability, efficiency, and effectiveness of online RL.

metaTextGrad: Automatically optimizing language model optimizers

Large language models (LLMs) are increasingly used in learning algorithms, evaluations, and optimization tasks. Recent studies have shown that using LLM-based optimizers to automatically optimize model prompts, demonstrations, predictions themselves, or other components can significantly enhance the performance of AI systems, as demonstrated by frameworks such as DSPy and TextGrad. However, optimizers built on language models themselves are usually designed by humans with manual design choices; optimizers themselves are not optimized. Moreover, these optimizers are general purpose by design, to be useful to a broad audience, and are not tailored for specific tasks. To address these challenges, we propose metaTextGrad, which focuses on designing a meta-optimizer to further enhance existing optimizers and align them to be good optimizers for a given task. Our approach consists of two key components: a meta prompt optimizer and a meta structure optimizer. The combination of these two significantly improves performance across multiple benchmarks, achieving an average absolute performance improvement of up to 6% compared to the best baseline.

Disentangling Reasoning and Knowledge in Medical Large Language Models

Medical reasoning in large language models (LLMs) aims to emulate clinicians' diagnostic thinking, but current benchmarks such as MedQA-USMLE, MedMCQA, and PubMedQA often mix reasoning with factual recall. We address this by separating 11 biomedical QA benchmarks into reasoning- and knowledge-focused subsets using a PubMedBERT classifier that reaches 81 percent accuracy, comparable to human performance. Our analysis shows that only 32.8 percent of questions require complex reasoning. We evaluate biomedical models (HuatuoGPT-o1, MedReason, m1) and general-domain models (DeepSeek-R1, o4-mini, Qwen3), finding consistent gaps between knowledge and reasoning performance. For example, m1 scores 60.5 on knowledge but only 47.1 on reasoning. In adversarial tests where models are misled with incorrect initial reasoning, biomedical models degrade sharply, while larger or RL-trained general models show more robustness. To address this, we train BioMed-R1 using fine-tuning and reinforcement learning on reasoning-heavy examples. It achieves the strongest performance among similarly sized models. Further gains may come from incorporating clinical case reports and training with adversarial and backtracking scenarios.

MedCaseReasoning: Evaluating and learning diagnostic reasoning from clinical case reports

Doctors and patients alike increasingly use Large Language Models (LLMs) to diagnose clinical cases. However, unlike domains such as math or coding, where correctness can be objectively defined by the final answer, medical diagnosis requires both the outcome and the reasoning process to be accurate. Currently, widely used medical benchmarks like MedQA and MMLU assess only accuracy in the final answer, overlooking the quality and faithfulness of the clinical reasoning process. To address this limitation, we introduce MedCaseReasoning, the first open-access dataset for evaluating LLMs on their ability to align with clinician-authored diagnostic reasoning. The dataset includes 14,489 diagnostic question-and-answer cases, each paired with detailed reasoning statements derived from open-access medical case reports. We evaluate state-of-the-art reasoning LLMs on MedCaseReasoning and find significant shortcomings in their diagnoses and reasoning: for instance, the top-performing open-source model, DeepSeek-R1, achieves only 48% 10-shot diagnostic accuracy and mentions only 64% of the clinician reasoning statements (recall). However, we demonstrate that fine-tuning LLMs on the reasoning traces derived from MedCaseReasoning significantly improves diagnostic accuracy and clinical reasoning recall by an average relative gain of 29% and 41%, respectively. The open-source dataset, code, and models are available at https://github.com/kevinwu23/Stanford-MedCaseReasoning.

Improving Model Alignment Through Collective Intelligence of Open-Source LLMS

Building helpful and harmless large language models (LLMs) requires effective model alignment approach based on human instructions and feedback, which necessitates high-quality human-labeled data. Constructing such datasets is often expensive and hard to scale, and may face potential limitations on diversity and generalization. To address these challenges, we introduce Mixture of Agents Alignment (MoAA), that leverages the collective strengths of various language models to provide high-quality data for model alignment. By employing MoAA, we enhance both supervised fine-tuning and preference optimization, leading to improved performance compared to using a single model alone to generate alignment data (e.g. using GPT-4o alone). Evaluation results show that our approach can improve win rate of LLaMA-3.1-8B-Instruct from 19.5 to 48.3 on Arena-Hard and from 22.33 to 57.23 on AlpacaEval2, highlighting a promising direction for model alignment through this new scalable and diverse synthetic data recipe. Furthermore, we demonstrate that MoAA enables a self-improvement pipeline, where models finetuned on MoA-generated data surpass their own initial capabilities, providing evidence that our approach can push the frontier of open-source LLMs without reliance on stronger external supervision. Data and code will be released.

Towards Artificial Intelligence Research Assistant for Expert-Involved Learning

Large Language Models (LLMs) and Large Multi-Modal Models (LMMs) have emerged as transformative tools in scientific research, yet their reliability and specific contributions to biomedical applications remain insufficiently characterized. In this study, we present \textbf{AR}tificial \textbf{I}ntelligence research assistant for \textbf{E}xpert-involved \textbf{L}earning (ARIEL), a multimodal dataset designed to benchmark and enhance two critical capabilities of LLMs and LMMs in biomedical research: summarizing extensive scientific texts and interpreting complex biomedical figures. To facilitate rigorous assessment, we create two open-source sets comprising biomedical articles and figures with designed questions. We systematically benchmark both open- and closed-source foundation models, incorporating expert-driven human evaluations conducted by doctoral-level experts. Furthermore, we improve model performance through targeted prompt engineering and fine-tuning strategies for summarizing research papers, and apply test-time computational scaling to enhance the reasoning capabilities of LMMs, achieving superior accuracy compared to human-expert corrections. We also explore the potential of using LMM Agents to generate scientific hypotheses from diverse multimodal inputs. Overall, our results delineate clear strengths and highlight significant limitations of current foundation models, providing actionable insights and guiding future advancements in deploying large-scale language and multi-modal models within biomedical research.

How Well Can General Vision-Language Models Learn Medicine By Watching Public Educational Videos?

Publicly available biomedical videos, such as those on YouTube, serve as valuable educational resources for medical students. Unlike standard machine learning datasets, these videos are designed for human learners, often mixing medical imagery with narration, explanatory diagrams, and contextual framing. In this work, we investigate whether such pedagogically rich, yet non-standardized and heterogeneous videos can effectively teach general-domain vision-language models biomedical knowledge. To this end, we introduce OpenBiomedVi, a biomedical video instruction tuning dataset comprising 1031 hours of video-caption and Q/A pairs, curated through a multi-step human-in-the-loop pipeline. Diverse biomedical video datasets are rare, and OpenBiomedVid fills an important gap by providing instruction-style supervision grounded in real-world educational content. Surprisingly, despite the informal and heterogeneous nature of these videos, the fine-tuned Qwen-2-VL models exhibit substantial performance improvements across most benchmarks. The 2B model achieves gains of 98.7% on video tasks, 71.2% on image tasks, and 0.2% on text tasks. The 7B model shows improvements of 37.09% on video and 11.2% on image tasks, with a slight degradation of 2.7% on text tasks compared to their respective base models. To address the lack of standardized biomedical video evaluation datasets, we also introduce two new expert curated benchmarks, MIMICEchoQA and SurgeryVideoQA. On these benchmarks, the 2B model achieves gains of 99.1% and 98.1%, while the 7B model shows gains of 22.5% and 52.1%, respectively, demonstrating the models' ability to generalize and perform biomedical video understanding on cleaner and more standardized datasets than those seen during training. These results suggest that educational videos created for human learning offer a surprisingly effective training signal for biomedical VLMs.