[Submitted on 30 Apr 2026 (v1), last revised 20 Oct 2026 (this version, v2)]
Abstract:How do CNN channels combine scene information into a class-specific response? We develop an input-conditioned adjoint inversion framework that renders individual channels and their combinations in pixel space. Lightweight Local Adjoint Correctors (LACs) calibrate backward signals through a frozen encoder, separating source-channel magnitude from spatial structure. Across four CNN backbones, individual deep-channel inversions retain global scene content, exhibiting a holographic organization that we describe as shared-scene superposition. Positive- and negative-weight class reconstructions each retain foreground and background content, yet their signed sum concentrates on the foreground. A decomposition into shared content and channel-specific residuals explains this recombination through destructive interference. Per-image spectra and reconstruction controls characterize this organization, while region-ranked channel ablations connect its spatial structure to class predictions. This account motivates covariance-volume channel selection (CovVol), which selects channels by the volume spanned by their centered global-average-pooled responses. We establish an exact squared-volume interpretation of the covariance determinant and derive its greedy selection rule. Compression, corruption, and transfer experiments demonstrate the practical value of this geometry. Applying LAC to a pure ViT-B/16 also improves input alignment over untrained LAC and raw vector-Jacobian products.
Submission history
From: Kaixiang Shu [view email]
[v1] Thu, 30 Apr 2026 07:32:07 UTC (5,316 KB)
[v2] Tue, 20 Oct 2026 11:32:49 UTC (34,616 KB)
