Towards Generalization in Subitizing with Neuro-Symbolic Loss using
  Holographic Reduced Representations
Mohammad Mahmudul Alam Edward Raff Tim Oates
While deep learning has enjoyed significant success in computer vision tasks
over the past decade, many shortcomings still exist from a Cognitive Science
(CogSci) perspective. In particular, the ability to subitize, i.e., quickly and
accurately identify the small (less than 6) count of items, is not well learned
by current Convolutional Neural Networks (CNNs) or Vision Transformers (ViTs)
when using a standard cross-entropy (CE) loss. In this paper, we demonstrate
that adapting tools used in CogSci research can improve the subitizing
generalization of CNNs and ViTs by developing an alternative loss function
using Holographic Reduced Representations (HRRs). We investigate how this
neuro-symbolic approach to learning affects the subitizing capability of CNNs
and ViTs, and so we focus on specially crafted problems that isolate
generalization to specific aspects of subitizing. Via saliency maps and
out-of-distribution performance, we are able to empirically observe that the
proposed HRR loss improves subitizing generalization though it does not
completely solve the problem. In addition, we find that ViTs perform
considerably worse compared to CNNs in most respects on subitizing, except on
one axis where an HRR-based loss provides improvement.