Title: Modularity Matters: Learning Invariant Relational Reasoning Tasks,
Abstract: We focus on two supervised visual reasoning tasks whose labels encode a
semantic relational rule between two or more objects in an image: the MNIST
Parity task and the colorized Pentomino task. The objects in the images undergo
random translation, scaling, rotation and coloring transformations. Thus these
tasks involve invariant relational reasoning. We report uneven performance of
various deep CNN models on these two tasks. For the MNIST Parity task, we
report that the VGG19 model soundly outperforms a family of ResNet models.
Moreover, the family of ResNet models exhibits a general sensitivity to random
initialization for the MNIST Parity task. For the colorized Pentomino task, now
both the VGG19 and ResNet models exhibit sluggish optimization and very poor
test generalization, hovering around 30% test error. The CNN we tested all
learn hierarchies of fully distributed features and thus encode the distributed
representation prior. We are motivated by a hypothesis from cognitive
neuroscience which posits that the human visual cortex is modularized, and this
allows the visual cortex to learn higher order invariances. To this end, we
consider a modularized variant of the ResNet model, referred to as a Residual
Mixture Network (ResMixNet) which employs a mixture-of-experts architecture to
interleave distributed representations with more specialized, modular
representations. We show that very shallow ResMixNets are capable of learning
each of the two tasks well, attaining less than 2% and 1% test error on the
MNIST Parity and the colorized Pentomino tasks respectively. Most importantly,
the ResMixNet models are extremely parameter efficient: generalizing better
than various non-modular CNNs that have over 10x the number of parameters.
These experimental results support the hypothesis that modularity is a robust
prior for learning invariant relational reasoning.