Representational Distortion, Similarity and the Universal Law of Generalization

Nick Chater and Ulrike Hahn

Abstract Psychological theories of similarity are typically defined over evry limited classes of representations. Geometric models represent objects as points in a multi dimensional space. Set-theoretic models represent objects as sets of features. We have recently developed an account of similarity, representational distortion, which can deal with arbitrary representations, and which includes geometric and set-theoretic accounts as special cases. The similarity between two representations is defined by the amount of distortion required to transform one representation into the other. This can be quantified using the mathematical theory of Kolmogorov complexity (Li & Vitanyi, 1993). This theory has a range of psychologically interesting properties. In particular, we show that the Universal Law of Generalization can be derived.