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On the Complexity of Bayesian Generalization
Yu-Zhe Shi · Manjie Xu · John Hopcroft · Kun He · Josh Tenenbaum · Song-Chun Zhu · Ying Nian Wu · Wenjuan Han · Yixin Zhu

Thu Jul 27 04:30 PM -- 06:00 PM (PDT) @ Exhibit Hall 1 #639

We examine concept generalization at a large scale in the natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated, focusing on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up and when the complexity of concepts becomes diverse. At the representational level, we investigate how the complexity varies when a visual concept is mapped to the representation space. Prior literature has shown that two types of complexities (Griffiths & Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun & Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm: 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 examine 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 rule-based generalization, while the trend is the opposite in similarity-based generalization.

Author Information

Yu-Zhe Shi (PersLab Research)
Manjie Xu (Beijing Institute of Technology)
John Hopcroft (Department of Computer Science, Cornell University)
Kun He (Huazhong University of Sceince and Technology)
Josh Tenenbaum (MIT)

Joshua Brett Tenenbaum is Professor of Cognitive Science and Computation at the Massachusetts Institute of Technology. He is known for contributions to mathematical psychology and Bayesian cognitive science. He previously taught at Stanford University, where he was the Wasow Visiting Fellow from October 2010 to January 2011. Tenenbaum received his undergraduate degree in physics from Yale University in 1993, and his Ph.D. from MIT in 1999. His work primarily focuses on analyzing probabilistic inference as the engine of human cognition and as a means to develop machine learning.

Song-Chun Zhu (UCLA)
Ying Nian Wu (UCLA)
Wenjuan Han (Beijing Jiaotong University)
Yixin Zhu (Peking University)

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