{"ID":2861460,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.01969","arxiv_id":"2510.01969","title":"Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions","abstract":"We consider adversarially robust classification in a multiclass setting under arbitrary loss functions and derive dual and barycentric reformulations of the corresponding learner-agnostic robust risk minimization problem. We provide explicit characterizations for important cases such as the cross-entropy loss, loss functions with a power form, and the quadratic loss, extending in this way available results for the 0-1 loss. These reformulations enable efficient computation of sharp lower bounds for adversarial risks and facilitate the design of robust classifiers beyond the 0-1 loss setting. Our paper uncovers interesting connections between adversarial robustness, $α$-fair packing problems, and generalized barycenter problems for arbitrary positive measures where Kullback-Leibler and Tsallis entropies are used as penalties. Our theoretical results are accompanied with illustrative numerical experiments where we obtain tighter lower bounds for adversarial risks with the cross-entropy loss function.","short_abstract":"We consider adversarially robust classification in a multiclass setting under arbitrary loss functions and derive dual and barycentric reformulations of the corresponding learner-agnostic robust risk minimization problem. We provide explicit characterizations for important cases such as the cross-entropy loss, loss fun...","url_abs":"https://arxiv.org/abs/2510.01969","url_pdf":"https://arxiv.org/pdf/2510.01969v1","authors":"[\"Camilo Andrés García Trillos\",\"Nicolás García Trillos\"]","published":"2025-10-02T12:42:36Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.OC\",\"stat.ML\"]","methods":"[]","has_code":false}