@inproceedings{chen2024exploring,
author = {Chen, Yinpeng and Chen, Dongdong and Dai, Xiyang and Liu, Mengchen and Feng, Yinan and Lin, Youzuo and Yuan, Lu and Liu, Zicheng},
title = {Exploring Invariance in Images through One-way Wave Equations},
booktitle = {ICML 2025},
year = {2024},
month = {October},
abstract = {In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with high fidelity from an initial condition. We demonstrate it using an intuitive encoder-decoder framework where each image is encoded into its corresponding initial condition (a single vector). Subsequently, the initial condition undergoes a specialized decoder, transforming the one-way wave equations into a first-order norm + linear autoregressive process. This process propagates the initial condition along the x and y directions, generating a high-resolution feature map (up to the image resolution), followed by a few convolutional layers to reconstruct image pixels. The revealed invariance, rooted in the shared wave equations, offers a fresh perspective for comprehending images, establishing a promising avenue for further exploration.},
url = {http://approjects.co.za/?big=en-us/research/publication/exploring-invariance-in-images-through-one-way-wave-equations/},
}