arXiv Machine Learning
Backpropagated Output Momentum: Relocating Optimizer History from Parameters to Task Space
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arXiv Machine Learning
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Activation-Keyed Momentum: An Anisotropic Momentum Update via the Delta Rule
The paper introduces Activation-Keyed Momentum (AK‑Momentum), a momentum update that uses the input activation of a linear layer as a key to apply a delta‑rule update, allowing each direction to decay at a rate proportional to its frequency of appearance. AK‑Momentum is proven to be a valid momentum, incorporates input‑side curvature correction without matrix inversion, and clears stale directions faster than traditional exponential moving average (EMA) under both fixed and drifting optima. It can replace the momentum buffer of any optimizer, scales with width under μP, adds only 22–25% extra compute, and demonstrates significant step‑count reductions in FineWeb‑Edu pretraining and other benchmarks. whyItMatters":"AK‑Momentum offers a principled, efficient way to adapt momentum decay to anisotropic training dynamics, improving convergence speed and stability across a range of models and datasets."
arXiv AI
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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.
arXiv Machine Learning
Aug 26
Delayed Optimizer-State Transport Shapes Short-Horizon Training Decisions
arXiv:2608.24593v1 Announce Type: new Abstract: Adaptive optimizers retain gradient history in moment variables, allowing a local change in loss weighting to alter later updates. We examine whether t...
arXiv Machine Learning
Jun 17
MGUP: A Momentum-Gradient Alignment Update Policy for Stochastic Optimization
arXiv:2606. 17526v1 Announce Type: new Abstract: Efficient optimization is essential for training large language models.
arXiv Machine Learning
Aug 21
DeltaMomentum: A Key-Value based Anisotropic Momentum Update via Delta Rule
arXiv:2608. 19491v1 Announce Type: new Abstract: Most modern optimizers form their momentum as an exponential moving average (EMA) of past gradients, forgetting every direction at one fixed rate.
arXiv Machine Learning
Aug 4
AOS: Adaptive Optimizer Switching via Training-State Signals for Faster Convergence and Better Generalization
arXiv:2608. 01997v1 Announce Type: new Abstract: Single-optimizer training is a poor fit for the distinct phases of deep network optimization: adaptive methods handle noisy early gradients well but overshoot flat minima, while SGD with momentum generalizes better in the late phase but converges slowly early on.