On the Complexity of Bayesian Generalization

TL;DR

This paper investigates how the complexity of visual concepts influences generalization in computational models, revealing that representation complexity affects rule- and similarity-based generalization differently, with implications for understanding visual cognition.

Contribution

It provides a computational analysis of how concept complexity impacts generalization modes and confirms the inverted-U relation between attribute representativeness and visual complexity.

Findings

High RoA attributes are used to describe concepts, with description length following an inverted-U relation.

High subjective complexity improves rule-based generalization performance.

Low subjective complexity favors similarity-based generalization.

Abstract

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the $complexity$ of concepts becomes diverse. Specifically, at the $representational \ level$, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the $computational \ level$, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.