Generative Compression

Status: Working Note Scope: Compact formal note on executable description as a distinct form of compression. Epistemic status: Conceptual framework with operational examples; not a theorem about minimal description length. Related files: - theory/emergence/trace-to-generator.md - theory/emergence/generative-form-systems.md - theory/core/mathematical-axioms.md Failure conditions: - Confusing lookup tables with explanations. - Overclaiming Kolmogorov complexity equivalence.

Definition: Generative compression is a compressed, executable description that can produce a target trace family and support prediction/variation under constraints.

Compared with standard compression: - Lossless/lossy codecs optimize reconstruction fidelity of a given trace. - Generative compression optimizes explanatory and predictive utility of an executable mechanism.

Examples: - Physical laws constraining trajectory families. - Grammar generating sentence classes. - IFS operators generating fractal-like image classes. - SuperCollider patch + runtime generating sound classes. - LLM weights/context/runtime generating response classes. - DNA + cellular runtime generating developmental trajectories.

Failure modes: - Lookup-table “compression” that only memorizes traces. - Overfit generators with no out-of-distribution robustness. - Non-causal generators that mimic outputs but fail interventions. - Non-robust generators sensitive to tiny runtime changes.