Dynamics of Stochastic Momentum with Sparse Updates in High Dimensions
Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics of two tractable models of momentum under sparse updates: a least squares model with sparse inputs and a logistic regression model with a rare class. Both admit exact closed-form second-moment dynamics whose high-dimensional limits we characterize across three scaling exponents for sparsity, batch size, and momentum decay. The phase structure on both problems is governed by the ratio of two intrinsic timescales: a momentum retention timescale (how many a...
| Authors | Katie Everett, Elliot Paquette |
|---|---|
| Primary category | stat.ML |
| Published | 27 May 2026 |
| Last updated at source | 27 May 2026 |
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