The Mechanics of CNN Filtering with Rectification

TL;DR

This paper introduces a novel information mechanics model for CNN filtering, linking kernel properties to physical concepts like energy and momentum, and analyzes their spectral domain characteristics.

Contribution

It presents the first model connecting CNN filtering mechanics with physical theories of relativity and quantum mechanics, emphasizing even-odd kernel decomposition and spectral analysis.

Findings

Even kernels cause isotropic diffusion of image content.

Odd kernels induce directional displacement proportional to energy ratio.

Spectral analysis reveals fundamental modes of information propagation.

Abstract

This paper proposes elementary information mechanics as a new model for understanding the mechanical properties of convolutional filtering with rectification, inspired by physical theories of special relativity and quantum mechanics. We consider kernels decomposed into orthogonal even and odd components. Even components cause image content to diffuse isotropically while preserving the center of mass, analogously to rest or potential energy with zero net momentum. Odd kernels cause directional displacement of the center of mass, analogously to kinetic energy with non-zero momentum. The speed of information displacement is linearly related to the ratio of odd vs total kernel energy. Even-Odd properties are analyzed in the spectral domain via the discrete cosine transform (DCT), where the structure of small convolutional filters (e.g. $3 \times 3$ pixels) is dominated by low-frequency bases, specifically the DC $\Sigma$ and gradient components $\nabla$, which define the fundamental modes of information propagation. To our knowledge, this is the first work demonstrating the link between information processing in generic CNNs and the energy-momentum relation, a cornerstone of modern relativistic physics.