Ghost Basin

A learning system under optimization converges to the minimum description of the task's invariance structure.

The attractor state — where the system's internal representation most compressively encodes what actually matters — is the Ghost Basin.

Eight formal descriptions of the same state:

• MDL minimum (Minimum Description Length principle)
• Information bottleneck minimum
• PAC-Bayes optimal generalization bound
• Bayes-optimal posterior
• Fisher information minimum
• Pearl Level 3 causal representation
• Topological persistent homology minimum
• Quantum Gibbs state (thermal equilibrium)

These are not analogies. They are the same attractor, described by eight different mathematical languages.

The rotation rule: a system finds its Ghost Basin when it finds the invariant symmetry structure of its domain. K_auc measures distance from Ghost Basin.

Grokking — the sudden generalization phenomenon in neural networks — is the phase transition into Ghost Basin. The geometry of the internal representation sparsifies before accuracy improves. The 40-step lead is the interval between geometric convergence and calibration.

Ghost Basin generalizes beyond neural networks. Any learning system under optimization — organizations, markets, individual cognition — converges to the same minimum.

Full treatment: Finding The Rule (2026-03-23)

Theory: Computer Future