compression-prediction-equivalence

IN premise — entries/2026/06/21/wiki-Machine_learning-chunk-2.md

Created 2026-06-21T09:55:50+00:00

Optimal prediction and optimal data compression are formally equivalent: an optimal predictor of sequence probabilities can be used for optimal compression via arithmetic coding, and vice versa

Dependents

These beliefs depend on this one:

• IN prediction-compression-manifold-unified-view — Prediction and compression are formally equivalent (Delétang et al., 2023), and the manifold hypothesis — that high-dimensional data lies on low-dimensional manifolds — offers a geometric explanation for why compression is effective in practice. Together, these ideas suggest a connection between learning, compression, and geometry, though the formal link between the manifold hypothesis and the prediction-compression equivalence is conceptual rather than proven.