{"ID":2825031,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.22055","arxiv_id":"2512.22055","title":"Why Smooth Stability Assumptions Fail for ReLU Learning","abstract":"Stability analyses of modern learning systems are frequently derived under smoothness assumptions that are violated by ReLU-type nonlinearities. In this note, we isolate a minimal obstruction by showing that no uniform smoothness-based stability proxy such as gradient Lipschitzness or Hessian control can hold globally for ReLU networks, even in simple settings where training trajectories appear empirically stable. We give a concrete counterexample demonstrating the failure of classical stability bounds and identify a minimal generalized derivative condition under which stability statements can be meaningfully restored. The result clarifies why smooth approximations of ReLU can be misleading and motivates nonsmooth-aware stability frameworks.","short_abstract":"Stability analyses of modern learning systems are frequently derived under smoothness assumptions that are violated by ReLU-type nonlinearities. In this note, we isolate a minimal obstruction by showing that no uniform smoothness-based stability proxy such as gradient Lipschitzness or Hessian control can hold globally...","url_abs":"https://arxiv.org/abs/2512.22055","url_pdf":"https://arxiv.org/pdf/2512.22055v1","authors":"[\"Ronald Katende\"]","published":"2025-12-26T15:17:25Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.OC\"]","methods":"[]","has_code":false}