| { |
| "paper_id": "QRtzkKrbJi", |
| "claims": [ |
| "The paper introduces a unified PDE gradient flow framework for distributionally robust optimization (DRO) with six concrete algorithms, including Wasserstein Gradient Flow (Algorithm 3) and Wasserstein Fisher-Rao flow (Algorithm 4) variants for entropy-regularized Wasserstein DRO (Section 4, Algorithms 3-4).", |
| "Proposition 1 shows the Wasserstein gradient flow sampler must run for time at least on the order of O((1/λ) log(L/√(λε))) to produce an ε-accurate gradient estimate (Section 4, Proposition 1).", |
| "Theorem 1 proves the outer loop of the gradient-flow-sampler-based DRO algorithm requires O(1/ε²_opt) iterations to reach an ε-stationary point (Section 5, Theorem 1).", |
| "Theorem 2 bounds the total computational complexity of the WGF-based DRO algorithm (Algorithm 3) as Õ(L_Φ L²_U L²_f d² / (λ³_U ε⁴_opt)) (Section 5, Theorem 2).", |
| "On CIFAR-10 adversarial training under PGD attacks, the WFR- and WGF-based DRO methods achieve consistently higher robust accuracy across all perturbation settings compared to baseline DRO methods (Section 6.3).", |
| "Lemma 1 establishes that the entropy-regularized DRO problem is equivalent to a Schrödinger half-bridge problem, enabling sampling from the conditional worst-case distribution (Section 3.1, Lemma 1)." |
| ], |
| "source": { |
| "v1_pdf_hash_exact": true, |
| "v1_source_hash_exact": true, |
| "current_pdf_hash_exact": true, |
| "current_source_hash_exact": true, |
| "v1_claim_anchors": 6, |
| "six_algorithm_labels": 6, |
| "rate_drift_detected": true |
| }, |
| "flow_time": { |
| "cells": 75, |
| "max_threshold_ratio_error": 4.440892098500626e-16, |
| "all_thresholds_pass": true, |
| "all_early_controls_fail": true |
| }, |
| "complexity": { |
| "cells": 48, |
| "outer_exponent": -1.9999999999999998, |
| "total_polynomial_exponent": -3.9999999999999996, |
| "max_outer_identity_error": 0.0, |
| "max_total_identity_error": 2.220446049250313e-16 |
| }, |
| "half_bridge": { |
| "cells": 9, |
| "max_fixed_marginal_error": 1.1102230246251565e-16, |
| "max_conditional_normalization_error": 2.220446049250313e-16, |
| "max_kkt_residual": 1.7763568394002505e-15, |
| "max_mixture_identity_error": 0.0 |
| }, |
| "cifar_source": { |
| "three_primary_figures": true, |
| "cifar_setup_present": true, |
| "wfr_wgf_source_conclusion_present": true |
| }, |
| "gates": { |
| "four_primary_hashes_exact": true, |
| "six_exact_live_claims": true, |
| "six_v1_claim_anchors": true, |
| "six_concrete_algorithms": true, |
| "material_rate_drift_detected": true, |
| "flow_time_grid_complete": true, |
| "flow_time_threshold_exact": true, |
| "early_flow_destructive_control": true, |
| "complexity_grid_complete": true, |
| "outer_rate_exponent": true, |
| "total_rate_exponent": true, |
| "complexity_identities_exact": true, |
| "half_bridge_grid_complete": true, |
| "half_bridge_fixed_marginal": true, |
| "half_bridge_gibbs_kkt": true, |
| "half_bridge_mixture_identity": true, |
| "three_primary_cifar_figures": true, |
| "cifar_setup_and_conclusion_pinned": true |
| }, |
| "all_gates_pass": true, |
| "scope": { |
| "literal_claim_source": "arXiv v1", |
| "current_revision": "material rate-drift control", |
| "cifar_results": "pinned primary figures and source conclusion; not independently rerun", |
| "finite_audits": "exact mechanisms and rate identities; not replacements for universal proofs" |
| } |
| } |
|
|
