Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration

ArXi:2605.13744v1 Announce Type: new Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between network equivariance and data symmetry remains largely heuristic. Particularly for real world data with imperfect symmetry, existing research lacks a systematic theoretical framework to quantify symmetry, select transformation groups, or evaluate model data alignment.