{"id":"51a1c42e-a51d-4169-89c3-7f46955b1100","arxiv_id":"2509.24894","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A rescaled SoftPlus family approximates LogSumExp with O(ρ) error, enabling stable stochastic optimization in entropic OT and KL-DRO.","lead":"This paper introduces a tunable approximation to the LogSumExp function, built on a modified 'safe KL' divergence, that preserves convexity and smoothness and can be optimized with stochastic gradients. Tests in optimal transport and distributionally robust optimization show fewer overflow failures and faster progress than standard baselines.","discovery_kind":"new_method","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-04T13:52:25.614275+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}