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A Unified Framework for the Mechanics of Information in Convolutional Neural Network Image Space

arXiv · AI, language, vision and robotics · article · Aug 26, 2026 · UTC

This paper introduces a unified mathematical framework for modeling information propagation through convolutional neural networks (CNNs), with the aim of connecting descriptions of physical space and information space. A correspondence is presented linking discrete filter symmetry and the relativistic energy--momentum relation under the widely used nonlinear rectified convolution operation. Specifically, symmetric filter components (e.g. the sum $Σ= [1,1]$) operate analogously to rest energy $mc^2$ in preserving the image centre of mass (e.g. isotropic diffusion), whereas antisymmetric compone

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