AIM Framework glossary

Effective Loop Gain

Canonical definition

Effective Loop Gain (GeffG{eff}). The Effective Loop Gain is the internal loop gain G≡\kappaS⋅β⋅γ⋅σ′(V∗)G \equiv \kappaS \cdot \beta \cdot \gamma \cdot \sigma'(V^{*}) reduced by the Knowledge Patch interception probability: Geff=G⋅(1−p(V,S))G{eff} = G \cdot (1 - p(V, S)). It is the fast-layer component of the Joint Loop Gain GjointG{joint} defined in Section A.5.6.

Explanation

The Effective Loop Gain is what the internal loop gain becomes after the Knowledge Patch has intercepted some fraction of M-driven actions at the I-Override gate. If the Patch intercepts nothing, the Effective Loop Gain equals the Internal Loop Gain and the loop runs at full strength. If the Patch intercepts everything, the Effective Loop Gain falls to zero and the loop is broken. In the joint fast-slow system, the Effective Loop Gain is only one of three components of the overall loop gain; the Slow-Layer Loop Gain, which carries the leading coupling between the fast and slow layers, and the higher-order cross-coupling remainder also contribute.

Epistemic status

Framework-Specific Parameter. Source: Appendix A.6.4, A.5.6.

Derivation

Appendix A, Section A.6.4; Chapter 13, Section 13.9.

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