  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.
