Uniform Stability and Generalization Error of GD and SGD on Fixed-Point Parameters
We analyze generalization error, uniform stability, and uniform argument stability of gradient descent (GD) and stochastic gradient descent (SGD) over discrete parameter spaces, where each update involves deterministic or stochastic rounding. We show that deterministic rounding degrades the generalization error of GD on convex, Lipschitz, and smooth loss functions, increasing the rate from $O(T/n)$ to $O(T/\sqrt{n})$, and establish matching lower bounds. We further prove that uniform stability of GD becomes $Ω(T)$, showing that stability-based generalization bounds are vacuous in this setting. In contrast, for the same losses, stochastic gradient descent with deterministic rounding admits...
| Authors | Jonghyun Shin, Sejun Park |
|---|---|
| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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