φ : Data → Compressibility Space
Foundation: Kolmogorov Complexity
// The shortest program that outputs x
Meaningful data has low Kolmogorov complexity — it can be described concisely. Noise cannot.
Most generative models start from noise and gradually "denoise" toward structure — powerful but inefficient. Comphi explores a different intuition: meaningful data lives on low-dimensional manifolds defined by compressibility.
By computing a Compression-ID (φ) — a vector capturing how data compresses through symmetry, edge distributions, texture sparsity, and learned codec rates — we map images into coordinates where coherent categories naturally cluster as islands.
Given a single example, we locate its position and navigate smoothly across the manifold, generating variations by steering in compressibility space rather than denoising through countless steps.
Start inside structure, not at random noise.
Categories emerge naturally, without labels.
Every coordinate in φ has meaning.
Noise is infinite. Meaning is compressible.
Comphi finds the islands of structure in an ocean of randomness.