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In this paper, we empirically reveal an invariance over images-images share aset of one-way wave equations with latent speeds. Each image is uniquelyassociated with a solution to these wave equations, allowing for itsreconstruction with high fidelity from an initial condition. We demonstrate itusing an intuitive encoder-decoder framework where each image is encoded intoits corresponding initial condition (a single vector). Subsequently, theinitial condition undergoes a specialized decoder, transforming the one-waywave equations into a first-order norm + linear autoregressive process. Thisprocess propagates the initial condition along the x and y directions,generating a high-resolution feature map (up to the image resolution), followedby a few convolutional layers to reconstruct image pixels. The revealedinvariance, rooted in the shared wave equations, offers a fresh perspective forcomprehending images, establishing a promising avenue for further exploration.

Exploring Invariance in Images through One-way Wave Equations