Summary
This paper (arXiv 2608.20295, Guan-Ju Peng) addresses uncertainty in sparse coding with learned dictionaries. After dictionary learning, sparse pursuit can yield exact atomic supports, but their physical interpretation is often not certified by calibration data—especially for highly coherent dictionaries, where alternative calibration-compatible dictionaries may assign different physical meanings to the same selected support. The work develops resolution-aware physical-support inference that jointly accounts for uncertainty in 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 deployment data resolve coherent-block interpretations and their atomic 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.
Paper Overview
Field: ML
Author: Guan-Ju Peng
Published: 2026-08-22
arXiv: 2608.20295
Abstract
Sparse pursuit after dictionary learning can produce exact atomic supports, even when their physical interpretation is not certified by calibration data—this is particularly true for highly coherent dictionaries, where alternative calibration-compatible dictionaries may assign different physical meanings to the same selected support. This paper develops resolution-aware physical-support inference that jointly considers uncertainty in the learned dictionary and the deployed signal representation.
Cross-dictionary confidence sets retain calibration-compatible dictionaries and deployment-compatible sparse representations, and then project the surviving interpretations into physical-support space. For locally coherent atom classes with separation scale s, once deployment data resolve coherent-block interpretations and their atomic 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 the active coefficients.
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