Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures

This paper introduces Presymplectification Networks (PSNs), a novel framework that restores non-degenerate symplectic geometry for constrained and dissipative mechanical systems by learning a symplectification lift via Dirac structures, thereby enabling accurate, structure-preserving long-term prediction of complex multibody dynamics like those of the ANYmal quadruped robot.

Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares + 1 more2026-03-06💻 cs

MuRating: A High Quality Data Selecting Approach to Multilingual Large Language Model Pretraining

MuRating is a scalable framework that transfers high-quality English data-quality signals to a unified multilingual evaluator via pairwise comparisons and translation, enabling the selection of balanced, high-quality datasets that significantly improve the performance of multilingual large language models on both English and non-English benchmarks.

Zhixun Chen, Ping Guo, Wenhan Han + 10 more2026-03-06💻 cs

Some Super-approximation Rates of ReLU Neural Networks for Korobov Functions

This paper establishes nearly optimal super-approximation error bounds of order 2m2m and 2m22m-2 in LpL_p and Wp1W^1_p norms, respectively, for ReLU neural networks approximating Korobov functions by leveraging sparse grid finite elements and bit extraction, thereby demonstrating that neural network expressivity effectively overcomes the curse of dimensionality.

Yuwen Li, Guozhi Zhang2026-03-06💻 cs

Kernel Based Maximum Entropy Inverse Reinforcement Learning for Mean-Field Games

This paper proposes a kernel-based maximum causal entropy inverse reinforcement learning framework for infinite-horizon stationary mean-field games that models unknown rewards in a reproducing kernel Hilbert space to capture nonlinear structures, proves the algorithm's theoretical consistency via Fréchet differentiability, and demonstrates superior policy recovery performance over linear baselines in traffic routing scenarios while extending the approach to finite-horizon non-stationary settings.

Berkay Anahtarci, Can Deha Kariksiz, Naci Saldi2026-03-06🔢 math