Does Sparse Connectivity Improve Generalization? Convolutional Networks Below the Edge of Stability
Gradient descent on overparameterized neural networks typically operates at the Edge of Stability (EoS), where the largest Hessian eigenvalue hovers around a step-size-dependent threshold. We study how sparse connectivity changes generalization below this threshold in two-layer ReLU networks. Prior results have shown that for fully-connected networks (FCNs), generalization guarantees in this regime degrade and become vacuous on high-dimensional spherical inputs. Our analysis reveals that sparse connectivity fundamentally alters this picture. Under sparse connectivity, the network processes a collection of low-dimensional patches rather than the full input vector, so the effective constrai...
| Authors | Tongtong Liang, Esha Singh, Rahul Parhi et al. |
|---|---|
| Primary category | stat.ML |
| Published | 5 March 2026 |
| Last updated at source | 7 May 2026 |
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