On the Complexity of Bayesian Generalization

Yu-Zhe Shi, Manjie Xu, Song-Chun Zhu, John E. Hopcroft, Kun He, Joshua B. Tenenbaum, Ying Nian Wu, Wenjuan Han, Yixin Zhu

Keywords: Bayesian Generalization, Rational Analysis

Abstract: We consider the concept generalization at a large scale in a diverse and natural visual spectrum. Established computational modes (\ie, rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study the 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 on visual complexity. Meanwhile, 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 having the potential to serve 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 opposite in the similarity-based generalization.

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TL;DR: Correlating the shift between rule- and similarity-based generalization with the subjective complexity of the natural visual world.

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