Xinxing Xu

Reinforcement learning for large language model reasoning often suffers from signal collapse: under uniform small-group sampling, difficult prompts frequently produce uninformative all-fail or all-success groups, causing useful gradients to disappear. We show that this failure is largely a statistical artifact of undersampling rather than an inherent limitation of the model. This suggests that sampling budget should be allocated adaptively across prompts according to their pass rates. We formalize this idea through a family of non-linear RL objectives, which induce difficulty-aware weighting and recover prior log-objective analyses as a special case. Based on this view, we propose Reinforce-Ada, with an estimation-based variant and a model-free sequential variant that adaptively allocate rollouts to recover informative signals. Across multiple models and math reasoning benchmarks, Reinforce-Ada consistently improves over standard GRPO baselines, recovering much of the benefit of large-group training at substantially lower cost.

Mathematical reasoning is widely regarded as a hallmark of human intelligence, and determining whether large language models (LLMs) can meaningfully perform it remains a central question in artificial intelligence and cognitive science. As LLMs are increasingly integrated into scientific workflows, rigorous evaluation of their mathematical capabilities becomes a practical necessity. Existing mathematical reasoning benchmarks, however, are often limited by synthetic problem settings and growing contamination from widely circulated datasets. We present LiveMathematicianBench, a dynamic multiple-choice benchmark for evaluating research-level mathematical reasoning using recent arXiv papers published after model training cutoffs. By grounding evaluation in newly published theorem statements, the benchmark provides a more realistic testbed for assessing whether models can reason about natural mathematical claims beyond memorized benchmark patterns. LiveMathematicianBench introduces a taxonomy of thirteen problem categories based on the logical form of theorem statements, enabling fine-grained evaluation across reasoning types such as implication, equivalence, existence, and uniqueness. It further introduces a proof-sketch-guided distractor generation pipeline, in which proof sketches are used to construct plausible but invalid answer choices that reflect misleading proof directions. This design makes the benchmark more sensitive to genuine mathematical understanding rather than surface-level answer matching. We additionally introduce a substitution-resistant evaluation mechanism designed to distinguish answer recognition from substantive mathematical reasoning. Evaluation of frontier models shows that the benchmark is far from saturated: the best-performing model, Gemini-3.1-pro-preview, achieves only 43.5\% accuracy in the standard setting. Under substitution-resistant evaluation, accuracy drops sharply across all models: GPT-5.4 achieves the highest score at 30.6\%, while Gemini-3.1-pro-preview falls to 17.6\%, below the 20\% random baseline. A dual-mode protocol comparing performance with and without proof-sketch access reveals that sketches yield consistent gains (e.g., +13.6 pp for Gemini-3.1-pro-preview), suggesting that models can leverage high-level proof strategies to improve reasoning. Overall, LiveMathematicianBench offers a scalable and contamination-resistant testbed for studying research-level mathematical reasoning in large language models.