Information Efficiency

Information efficiency η is the fraction of mutual information with ground truth that a processing step preserves under its probabilistic (stochastic) component. η = 1 — deterministic: same inputs always produce the same output; no extra entropy from randomness. η < 1 — probabilistic model, noisy channel, or inconsistent cross-stream join.

η = 1 does not mean the step is L0 or lossless toward concrete ground truth. Logical inference and other generalizing deterministic transforms are typically L1 or L2 and strictly lossy under the data processing inequality even at η = 1 — the conclusion forgets which specific L0 instances supported it unless the contract carries them.

Along a chain, efficiencies multiply:

I(Output ; Ground_Truth) ≤ I(Input ; Ground_Truth) × η₁ × η₂ × … × ηₙ

Three steps at η = 0.9 retain ≈ 0.73 — the formal content of “uncertainty compounds multiplicatively” in The Facets Composed. Frozen collective subjectivity can produce directional loss (bias), not just noise that averages out.

Published per-step η (or equivalent) belongs in the epistemic uncertainty contract alongside temporal and cross-stream components.

Corpus stance

A1 — adopted on this site: Operational shorthand for probabilistic computation loss; grounded in Shannon via What Information Theory Says.