arXiv Machine Learning
OrScale: Orthogonalised Optimization with Layer-Wise Trust-Ratio Scaling
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arXiv Machine Learning
Jun 25
Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors
arXiv:2606. 25971v1 Announce Type: new Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object.
arXiv Machine Learning
Sep 24
The Drift Contract: Spectral Updates for Depth-Robust Local Learning
The paper introduces the Drift Contract, a spectral update geometry for local learning that improves depth robustness and hyperparameter stability. By applying momentum orthogonalization with spectral step scaling to per‑layer updates, the authors achieve consistent performance across a wide range of widths and depths on CIFAR‑10 MLPs, outperforming local Adam and providing a per‑layer, input‑conditioned drift bound. The study also shows that the spectral geometry itself, rather than step‑size rules, drives the observed depth robustness, while a negative result indicates that the stability benefit is limited to non‑normalized layers.
arXiv AI
Jun 4
Spectral Scaling Laws of Muon
arXiv:2606. 04058v1 Announce Type: cross Abstract: Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon.
arXiv AI
Oct 7
Does Muon Need Fine-Grained Spectral Shaping?
The paper investigates how much spectral detail is necessary for the Muon optimizer, which traditionally uses a flat spectral profile. By analyzing singular modes, the authors find that most modes lie below a noise edge yet align positively with the gradient, leading them to propose BulkBoost—a two‑band spectral reweighting framework that adjusts bulk and spike gains while preserving matrix norms. Experiments across various pre‑training settings show that this low‑dimensional reweighting matches or surpasses fine‑grained spectral profiles, achieving notable loss reductions.
arXiv Machine Learning
Jul 28
The Intruder Threshold: A Spectral Law for LoRA Fine-Tuning
arXiv:2607. 23711v1 Announce Type: new Abstract: LoRA fine-tuning can create intruder dimensions: new leading singular vectors of the updated weight matrix $W+BA$ that are nearly orthogonal to all pretrained singular vectors and that drive catastrophic forgetting.
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.