AdjointBackMapV2: Precise Reconstruction of Arbitrary CNN Unit's Activation via Adjoint Operators

TL;DR

This paper introduces AdjointBackMapV2, a novel method that uses adjoint operators and extended input spaces to accurately reconstruct the activation hypersurfaces of arbitrary CNN units, improving interpretability.

Contribution

It extends previous adjoint operator methods by including bias in the input space, enabling precise reconstruction of CNN unit activations for any layer and unit.

Findings

Achieves near-zero reconstruction error on CIFAR-10 and CIFAR-100 datasets.

Provides a mathematically proven method for exact activation reconstruction.

Enhances understanding of CNN inner workings through hypersurface mapping.

Abstract

Adjoint operators have been found to be effective in the exploration of CNN's inner workings [1]. However, the previous no-bias assumption restricted its generalization. We overcome the restriction via embedding input images into an extended normed space that includes bias in all CNN layers as part of the extended space and propose an adjoint-operator-based algorithm that maps high-level weights back to the extended input space for reconstructing an effective hypersurface. Such hypersurface can be computed for an arbitrary unit in the CNN, and we prove that this reconstructed hypersurface, when multiplied by the original input (through an inner product), will precisely replicate the output value of each unit. We show experimental results based on the CIFAR-10 and CIFAR-100 data sets where the proposed approach achieves near 0 activation value reconstruction error.