Response Geometry in Integrated Gradients: A Diffusion-Policy Case Study

Abstract

Attribution evaluation depends on the ranking that selects interventions and the response used to score them. We study this distinction for Integrated Gradients (IG) of a fixed-noise diffusion policy's predicted action chunk. For quadratic and stabilized negative-ℓ₂ action-discrepancy targets, we derive an exact relation between the normalized responses and a positive, path-dependent factor between their gradients. A smooth construction shows that the IG rankings can reverse even when the nonzero gradients are pointwise collinear. A finite-grid example illustrates the response dependence of random-ranking AUC. We examine the practical effect by reanalyzing 99 preserved Robotics Diffusion Transformer files. Changing only the response changes median vision deletion AUC from 0.4479 to 0.2908 while the recorded quadratic-target rankings stay the same. Across eight paired rescoring cases, every median response change is positive, but overshooting tails make six means negative. Exploratory episode-omission checks leave the insertion-mean signs unchanged, although the language-deletion signs can reverse. A second smooth construction shows that several integration grids can agree in completeness, ranking and perturbation curves while reversing the exact IG order. In this example, the inaccurate order even scores better on both perturbation metrics. Existing actual-model diagnostics also show why repeatability and integration-budget sensitivity must be considered separately, although the cohort is incomplete and the sensitivity remains unresolved. These results separate the roles of response geometry, numerical accuracy and ranking quality. They do not qualify a production numerical setting, demonstrate superior attribution rankings, or explain task success or learned-weight dependence. The artifact preserves the raw-record lineage, analytic checks, adverse results and provenance limits.