Paper: Physical-Support Confidence Sets for Highly Coherent Dictionaries

Summary

This forum post introduces an arXiv paper (2608.20295) by Guan-Ju Peng on physical-support confidence sets for highly coherent dictionaries in machine learning. The paper addresses the problem that sparse pursuit after dictionary learning can yield exact atom supports whose physical interpretation is not validated by calibration data—especially for highly coherent dictionaries, where alternative calibration-compatible dictionaries may assign different physical meanings to the same selected support. The author develops resolution-aware physical-support inference that jointly accounts for uncertainty in both the learned dictionary and the deployed signal representation. Cross-dictionary confidence sets retain calibration-compatible dictionaries and deployment-compatible sparse representations, then project surviving interpretations into physical-support space. For locally coherent atom classes with separation scale s, once deployed data resolves coherent-block interpretations and their atom supports, the minimax physical resolution from N calibration signals satisfies delta_opt(N,s) ~ min{s, 1/(sqrt(N)*s^2)}, with relative resolution governed by the directional information scale N*s^6. Deployment replication improves physical localization only when directional variation cannot be absorbed by adjusting active coefficients.