Quantum Analogical Modeling with Homogeneous Pointers

TL;DR

This paper introduces a revised quantum analogical modeling approach that uses homogeneous pointers to efficiently identify exemplar groups, improving behavior prediction by focusing on contextually consistent exemplars.

Contribution

It simplifies homogeneity determination in Quantum Analogical Modeling by using pointers, enhancing the model's efficiency and accuracy in exemplar-based predictions.

Findings

Homogeneity can be determined by checking for heterogeneous pointers.

The revised method improves the identification of homogeneous supracontexts.

The approach aligns with quantum mechanics principles in uncertainty measurement.

Abstract

Quantum Analogical Modeling (QAM) works under the assumption that the correct exemplar-based description for a system of behavior minimizes the overall uncertainty of the system. The measure used in QAM differs from the traditional logarithmic measure of uncertainty; instead QAM uses a quadratic measure of disagreement between pairs of exemplars. (This quadratic measure parallels the squaring function holding between the amplitude and the probability for a state function in quantum mechanics.) QAM eliminates all supracontexts (contextual groupings of exemplars) that fail to minimize the number of disagreements. The resulting system thus distinguishes between homogeneous and heterogeneous supracontexts and uses only exemplars in homogeneous supracontexts to predict behavior. This paper revises earlier work on QAM (in 2005) by showing that homogeneity for a supracontext can be most simply determined by discovering whether there are any heterogeneous pointers between any of the supracontext's exemplars. A pointer for a pair of exemplars is heterogeneous whenever those two exemplars are found in different subcontexts of the supracontext and take different outcomes.