# The Mechanics of CNN Filtering with Rectification

arXiv: https://arxiv.org/abs/2512.24338 · HTML: https://mlsanity.com/paper/2512.24338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Space](https://mlsanity.com/paper/2412.15032/) (2024)
- [PDE-based Group Equivariant Convolutional Neural Networks](https://mlsanity.com/paper/2001.09046/) (2020)
- [Exact conservation laws for neural network integrators of dynamical systems](https://mlsanity.com/paper/2209.11661/) (2022)
- [The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning](https://mlsanity.com/paper/2103.04913/) (2021)
- [Unveiling the Unseen: Identifiable Clusters in Trained Depthwise Convolutional Kernels](https://mlsanity.com/paper/2401.14469/) (2024)
- [On Symmetries in Convolutional Weights](https://mlsanity.com/paper/2503.19215/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Unified Framework for the Mechanics of Information in Convolutional Neural Network Image Space](https://mlsanity.com/paper/2608.26363/) (2026)

## Abstract (arXiv)

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 × 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.