arXiv:2608. 02991v1 Announce Type: new Abstract: Matrix spectral optimizers reshape weight-update spectra but usually delegate vector-valued biases to a separate optimizer.
arXiv:2603. 28921v3 Announce Type: replace-cross Abstract: The critical damping condition of the damped harmonic oscillator model of SGD with momentum (Qian, 1999) yields a momentum schedule with no tuned hyperparameters: mu(t) = 1 - 2*sqrt(alpha(t)).
arXiv:2607. 22927v1 Announce Type: new Abstract: Weights and biases are normally optimized as separate parameter tensors, yet they do not represent separate functions when the input to an affine layer has nonzero mean.
AF‑Muon is an AdamW‑free extension of the Muon optimizer that retains Muon’s matrix update for hidden weights while applying a support‑aware finite‑cap linear minimization oracle to tied vocabulary tables and an RMS‑normalized update for one‑dimensional auxiliary parameters. This design eliminates second‑moment state, reducing optimizer‑state memory by about 20% compared to Hybrid Muon. Across nine tied‑token settings—including decoder‑only language models, T5‑style encoder‑decoders, and ImageGPT‑style variants—AF‑Muon consistently improves mean validation loss and perplexity over both Hybrid Muon and a SCION‑style Sign endpoint, with robust gains confirmed by long‑horizon runs and hyperparameter studies.
The paper investigates why the orthogonal optimiser Muon outperforms Adam in large language model pretraining by analysing the spectral properties of Transformer loss landscapes. It finds that Muon’s momentum buffers exhibit an anisotropic spectral profile with a volatile head and a tolerant bulk, enabling larger effective step sizes. Building on this insight, the authors propose Spectral‑Aware Muon (SAMuon) and a lightweight variant, which adjust the bulk scaling while keeping the head unchanged, achieving 13–24 % fewer training tokens than Muon without extra FLOPs.
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:2607. 19331v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood.
arXiv:2605.07815v2 Announce Type: replace Abstract: Muon fixes the \emph{direction} of every matrix-valued update at the polar factor of its momentum, while each layer's step \emph{magnitude} is addr...
The paper studies how different optimizers perform as training duration (overtraining) increases, focusing on matrix‑preconditioned methods (Muon, SOAP) and a momentum‑scheduled method (ADANA) compared to AdamW. Across models ranging from 51M to 253M parameters and overtraining factors up to 256×, the authors find that optimal learning‑rate schedules, weight‑decay coefficients, and memory settings shift with horizon, and that ADANA consistently outperforms AdamW, especially with log‑time weight decay and momentum cooldown. Muon and SOAP maintain roughly constant token‑efficiency advantages, with SOAP potentially improving at the highest overtraining levels.
arXiv:2609.14715v1 Announce Type: new Abstract: We scale our conventional sub-150M pretraining recipe from 53.5M to 109.7M parameters, holding the method fixed (Qwen3-style decoder with grouped-query...
arXiv:2609.00762v1 Announce Type: new Abstract: Parameter-efficient fine-tuning is usually framed as a question of how many parameters to update. Under a severe trainable-state budget, however, where...
arXiv:2607. 14516v1 Announce Type: new Abstract: Interpreting optimizers as gradient-flow discretizations has motivated applying higher-order Runge-Kutta (RK) integrators to neural networks.
arXiv:2608. 04407v1 Announce Type: cross Abstract: Memory-efficient matrix optimizers such as Sinkhorn gradient descent remove most AdamW optimizer state for dense Transformer matrices, but direct application to Mixture-of-Experts (MoE) training is unreliable.