AIM Framework glossary

Restriction-Induced Concentration Factor

Canonical definition

Restriction-Induced Concentration Factor ( $\rho(\mathcal{H})$ ). The Restriction-Induced Concentration Factor is a scalar measure of the degree to which a restricted Hypothesis Space concentrates the Bayesian posterior relative to the unrestricted posterior. Two operationalisations are tractable: the KL-divergence form $\rho(\mathcal{H}) = \exp(D{KL}(P^{}\|P^{\mathcal{H}}))$ , where $P^{}$ is the unrestricted posterior over the full $\mathcal{H}^{}$ (including $HM$ ) and $P^{\mathcal{H}}$ is the restricted posterior; and the dimensionality form $\rho(\mathcal{H}) = |\mathcal{H}^{}|/|\mathcal{H}|$ . Both make $\rho = 1$ when no restriction applies and $\rho > 1$ when the Hypothesis Space omits relevant Hypotheses.

Explanation

This factor measures how much damage the missing Hypothesis does to your Belief system. If you have all the relevant Hypotheses available (including "this wanting might be mimetically driven"), then the factor is one and there is no distortion. If the M-Hypothesis is absent from your Hypothesis set, then the Bayesian posterior is forced to assign all of that Hypothesis's probability mass to the remaining ones, concentrating the posterior on explanations the unrestricted analysis would deprecate. The larger the concentration, the larger the factor, and the larger the Slow-Layer Loop Gain. AIM Vocabulary Acquisition reduces the factor by adding the M-Hypothesis to the Hypothesis set, which is one of the two slow-layer channels through which the Knowledge Patch operates.

Epistemic status

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

Derivation

Appendix A, Section A.5.6.

Canonical definition

Explanation

Epistemic status

Derivation

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