Similarity, feature discovery, and the size principle

Area of Science:

• Cognitive Science
• Psychology
• Artificial Intelligence

Background:

• The size principle posits that rare features are weighted more heavily than common features in similarity evaluations.
• This principle is supported by Bayesian analyses of induction and relates to universal laws of generalization.

Purpose of the Study:

• To demonstrate that the size principle can be derived from representational optimality.
• To empirically test the size principle's agreement with human judgments across diverse datasets.

Main Methods:

• Derivation of the size principle from a representational optimality framework.
• Analysis of human similarity judgments across 11 datasets (animals, artifacts).

Main Results:

• The size principle was shown to be a consequence of representational optimality.
• Human judgments on featural similarity across animal and artifact domains aligned with the 1/n scaling law.

Conclusions:

• The size principle is a robust finding supported by both theoretical derivation and empirical evidence.
• This principle has significant implications for understanding human cognition and developing AI systems.