Knowledge as Orbit: Finite Collections as Phases of an Exactly Periodic Latent Generator

The paper proposes storing finite collections of knowledge as the orbit of a single compact latent generator that cycles exactly back to its starting point. By encoding each item as a phase of a fixed rotation in a learned latent space and decoding all phases with a shared network, the method guarantees exact closure through a discrete Fourier operator. Experiments on images and video clips show that this exactly periodic operator outperforms general learned or norm‑preserving operators, achieving comparable or better fidelity while eliminating visible seams and enabling efficient compression.