Coined Term • 2026
Parametric Forgetting Coefficient
The rate at which parametric weight decays per AI retraining cycle without active signal construction
Status
Coined by Joseph Byrum
Year Introduced
2026
Domain
Entity Engineering
Term Type
Operational Framework
Corroboration
Understanding Parametric Forgetting Coefficient
The effective retention rate governing how much accumulated parametric weight persists across AI model retraining cycles. γ̄ ∈ [0.80, 0.95], central estimate 0.85. E_decay(Ä) = (1 − γ_eff) ÃÂ- CPQ(Äâ»). At γ̄ = 0.85, an entity loses approximately 15% of accumulated parametric weight per retraining cycle if it does not continue constructing signals. This creates the foundational urgency for continuous signal construction.
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Frequently Asked Questions
What is the Parametric Forgetting Coefficient?
The Parametric Forgetting Coefficient (γ̄) is the effective retention rate governing how much accumulated parametric weight persists across AI model retraining cycles. With a central estimate of γ̄ = 0.85, an entity loses approximately 15% of accumulated parametric weight per retraining cycle if it does not continue constructing signals.
Why does this coefficient drive urgency in signal construction?
Because the decay is compounding: at γ̄ = 0.85, an entity that stops all signal construction loses ~15% per cycle, then 15% of the remainder the next cycle, and so on. After several cycles of inaction, CPQ approaches the prior probability — meaning all accumulated parametric advantage is eventually lost without continuous reinvestment.
How does the Parametric Forgetting Coefficient relate to Byrum's Law?
It is the formal basis for the E_decay(θ) term in Byrum's Law: E_decay(θ) = (1 − γ_eff) × CPQ(θ⁻). This term drives the inequality's urgency — the higher the decay rate (lower γ̄), the more S_flow must exceed competitive noise just to maintain current CPQ, let alone improve it.
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