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
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:7781-7815, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-chen25g, title = {Exploring Invariance in Images through One-way Wave Equations}, author = {Chen, Yinpeng and Chen, Dongdong and Dai, Xiyang and Liu, Mengchen and Feng, Yinan and Lin, Youzuo and Yuan, Lu and Liu, Zicheng}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {7781--7815}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/chen25g/chen25g.pdf}, url = {https://proceedings.mlr.press/v267/chen25g.html}, 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.} }
Endnote
%0 Conference Paper %T Exploring Invariance in Images through One-way Wave Equations %A Yinpeng Chen %A Dongdong Chen %A Xiyang Dai %A Mengchen Liu %A Yinan Feng %A Youzuo Lin %A Lu Yuan %A Zicheng Liu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-chen25g %I PMLR %P 7781--7815 %U https://proceedings.mlr.press/v267/chen25g.html %V 267 %X 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.
APA
Chen, Y., Chen, D., Dai, X., Liu, M., Feng, Y., Lin, Y., Yuan, L. & Liu, Z.. (2025). Exploring Invariance in Images through One-way Wave Equations. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:7781-7815 Available from https://proceedings.mlr.press/v267/chen25g.html.

Related Material