Exploring Invariance in Images through One-way Wave Equations
Yinpeng Chen, Dongdong Chen, Xiyang Dai, Mengchen Liu, Yinan Feng, Youzuo Lin, Lu Yuan, Zicheng Liu
Abstract
In this paper, we empirically demonstrate that natural images can be reconstructed with high fidelity from compressed representations using a simple first-order norm-plus-linear autoregressive (FINOLA) process—without relying on explicit positional information. Through systematic analysis, we observe that the learned coefficient matrices ($\mathbf{A}$ and $\mathbf{B}$) in FINOLA are typically invertible, and their product, $\mathbf{AB}^{-1}$, is diagonalizable across training runs. This structure enables a striking interpretation: FINOLA’s latent dynamics resemble a system of one-way wave equations evolving in a compressed latent space. Under this framework, each image corresponds to a unique solution of these equations. This offers a new perspective on image invariance, suggesting that the underlying structure of images may be governed by simple, invariant dynamic laws. Our findings shed light on a novel avenue for understanding and modeling visual data through the lens of latent-space dynamics and wave propagation.
BibTeX
@inproceedings{
chen2025exploring,
title={Exploring Invariance in Images through One-way Wave Equations},
author={Yinpeng Chen and Dongdong Chen and Xiyang Dai and Mengchen Liu and Yinan Feng and Youzuo Lin and Lu Yuan and Zicheng Liu},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=HdogAuhlD5}
}