arXiv Machine Learning
Jun 9

Token Sample Complexity of Attention

arXiv:2512. 10656v3 Announce Type: replace Abstract: As context windows in large language models continue to expand, it is essential to characterize how attention behaves at extreme sequence lengths.

By L\'ea Bohbot, Cyril Letrouit, Gabriel Peyr\'e, Fran\c{c}ois-Xavier Vialard
arXiv AI
Aug 25

A Physical Response-and-Memory Model for Muon Optimization

The paper introduces a physical response-and-memory model for the Muon optimizer, explaining its semi‑orthogonalized momentum update as the maximally dissipative direction under an output‑side safety budget. It treats the weight matrix as a responsive medium with internal stress, showing that momentum corresponds to accumulated stress whose relaxation occurs over multiple timescales—fast and slow. Based on this, the authors propose the Bi‑Maxwell optimizer, which uses a two‑timescale memory kernel and achieves target loss in fewer steps on a public large‑language‑model benchmark.

By Yinze Hu, Hongjun Xiang, Xingao Gong, Hongyu Yu