Visual Invariance from Image-Driven Dynamics

We introduce a computer vision framework where a continuous linear dynamical system (formulated as a PDE) transforms static image pixel arrays into temporal spectral functions for sampling, pooling, and classification. Evaluated on the MNIST handwritten digit dataset, our model is trained strictly on standard upright samples yet demonstrates robust generalization to test samples subjected to severe, unseen geometric transformations—including rotation, anisotropic scaling, shearing, and elastic warping. Unlike prior approaches, our framework requires no a priori knowledge of the test-time transformations or brute-force data augmentation. Furthermore, continuous PDE dynamics offer a biologically plausible alternative to standard discrete spatial processing, suggesting that continuous dynamical evolution can establish stable feature trajectories across neural network architectures more efficiently than conventional iterative mechanisms.