Researchers have proposed a physical model for optimizing weight updates during deep learning training. The model treats the weight matrix as a responsive medium with memory and explains why semi-orthogonalization in Muon optimization works. The authors also propose a new optimizer called Bi-Maxwell, which combines two timescales to improve training efficiency. Experiments on a public benchmark show that replacing the single timescale memory kernel with a two-timescale version can lead to faster convergence to the target loss. --- Why it matters: This matters because it provides a deeper understanding of why certain optimization techniques work and how they can be improved. The proposed model and optimizer have practical implications for training large language models, which are increasingly important in applications such as natural language processing and text generation. Source: https://arxiv.org/abs/2608.22994