Adjoint Inversion Reveals Holographic Superposition and Destructive Interference in CNN Classifiers

TL;DR

This paper introduces a novel inversion framework that reveals CNN classifiers operate via destructive interference, challenging the traditional Spatial Funnel Hypothesis and providing new insights into model interpretability and OOD failure.

Contribution

It presents a hallucination-free inversion method that uncovers pixel-level superposition and interference in CNNs, with a covariance-volume channel selection algorithm and OOD failure analysis.

Findings

CNN encoders exhibit strong superposition at pixel level.

Classification results from interference of channels rather than background suppression.

Covariance volume collapse correlates with out-of-distribution failures.

Abstract

A foundational assumption in CNN interpretability -- that deep encoders suppress background pixels while classifiers merely select from a cleaned feature pool (the Spatial Funnel Hypothesis) -- remains untested due to spatial hallucinations in existing visualization tools. We address this by introducing a hallucination-free inversion framework built on magnitude-phase decoupling and Local Adjoint Correctors. Our method mathematically guarantees that the spatial gradient support of every reconstruction stems strictly from genuinely active channels. Using this framework as a geometric probe, we uncover the first pixel-level evidence of strong superposition in vision encoders. We show that per-channel inversions are uniformly holographic: positive and negative weight reconstructions are visually and energetically indistinguishable. However, their algebraic sum sharply concentrates on the foreground. This proves classification operates via destructive interference -- classifier weights cancel a shared background direction in pixel space and constructively assemble class-discriminative residuals, directly falsifying the Spatial Funnel Hypothesis. This interference model identifies the volume of the admissible interference subspace as the geometric quantity governing channel requirements. We prove this volume is dual to the GAP covariance determinant, yielding a covariance-volume channel selection algorithm with a $(1-1/e)$ approximation guarantee. This algorithm mathematically reveals out-of-distribution (OOD) failure as a measurable collapse of the covariance volume essential for interference-based classification. Our framework extends seamlessly to attention-based heads without retraining.