{"ID":2867525,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.17413","arxiv_id":"2509.17413","title":"Distributionally Robust Safety Verification of Neural Networks via Worst-Case CVaR","abstract":"Ensuring the safety of neural networks under input uncertainty is a fundamental challenge in safety-critical applications. This paper builds on and expands Fazlyab's quadratic-constraint (QC) and semidefinite-programming (SDP) framework for neural network verification to a distributionally robust and tail-risk-aware setting by integrating worst-case Conditional Value-at-Risk (WC-CVaR) over a moment-based ambiguity set with fixed mean and covariance. The resulting conditions remain SDP-checkable and explicitly account for tail risk. This integration broadens input-uncertainty geometry-covering ellipsoids, polytopes, and hyperplanes-and extends applicability to safety-critical domains where tail-event severity matters. Applications to closed-loop reachability of control systems and classification are demonstrated through numerical experiments, illustrating how the risk level $\\varepsilon$ trades conservatism for tolerance to tail events-while preserving the computational structure of prior QC/SDP methods for neural network verification and robustness analysis.","short_abstract":"Ensuring the safety of neural networks under input uncertainty is a fundamental challenge in safety-critical applications. This paper builds on and expands Fazlyab's quadratic-constraint (QC) and semidefinite-programming (SDP) framework for neural network verification to a distributionally robust and tail-risk-aware se...","url_abs":"https://arxiv.org/abs/2509.17413","url_pdf":"https://arxiv.org/pdf/2509.17413v1","authors":"[\"Masako Kishida\"]","published":"2025-09-22T07:04:53Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}