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 $Σ$ 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.

翻译：本文受狭义相对论与量子力学物理理论的启发，提出基础信息力学作为理解带整流操作的卷积滤波力学性质的新模型。我们将卷积核分解为正交的偶分量与奇分量：偶分量使图像内容各向同性扩散并保持质心不变，类比于净动量为零的静止或势能状态；奇分量则引起质心的定向位移，类比于具有非零动量的动能。信息位移的速度与奇分量能量占总能量的比值呈线性关系。通过离散余弦变换（DCT）在频域分析偶-奇特性，发现小型卷积滤波器（如 $3 \times 3$ 像素）的结构主要由低频基主导，特别是直流分量 $Σ$ 与梯度分量 $\nabla$，它们定义了信息传播的基本模式。据我们所知，本研究首次揭示了通用卷积神经网络中的信息处理与能量-动量关系（现代相对论物理的基石）之间的理论联系。