We study convergence properties of the discrete-time Mean-Field Langevin Stochastic Gradient Descent-Ascent (MFL-SGDA) algorithm for solving distributional minimax optimization. These problems arise in various applications, such as zero-sum games, generative adversarial networks and distributionally robust learning. Despite the significance of MFL-SGDA in these contexts, the discrete-time convergence rate remains underexplored. To address this gap, we establish a last-iterate convergence rate of $O(\frac{1}{\epsilon}\log\frac{1}{\epsilon})$ for MFL-SGDA. This rate is nearly optimal when compared to the complexity lower bound of its Euclidean counterpart. This rate also matches the complexity of mean-field Langevin stochastic gradient descent for distributional minimization and the outer-loop iteration complexity of an existing double-loop algorithm for distributional minimax problems. By leveraging an elementary analysis framework that avoids PDE-based techniques, we overcome previous limitations and achieve a faster convergence rate.

Current benchmarks for evaluating the reasoning capabilities of Large Language Models (LLMs) face significant limitations: task oversimplification, data contamination, and flawed evaluation items. These deficiencies necessitate more rigorous assessment methods. To address these limitations, we introduce PHYBench, a benchmark of 500 original physics problems ranging from high school to Physics Olympiad difficulty. PHYBench addresses data contamination through original content and employs a systematic curation pipeline to eliminate flawed items. Evaluations show that PHYBench activates more tokens and provides stronger differentiation between reasoning models compared to other baselines like AIME 2024, OlympiadBench and GPQA. Even the best-performing model, Gemini 2.5 Pro, achieves only 36.9\% accuracy compared to human experts' 61.9\%. To further enhance evaluation precision, we introduce the Expression Edit Distance (EED) Score for mathematical expression assessment, which improves sample efficiency by 204\% over binary scoring. Moreover, PHYBench effectively elicits multi-step and multi-condition reasoning, providing a platform for examining models' reasoning robustness, preferences, and deficiencies. The benchmark results and dataset are publicly available at https://www.phybench.cn/.