Towards Generalization in Subitizing with Neuro-Symbolic Loss using Holographic Reduced Representations

TL;DR

This paper introduces a neuro-symbolic loss function using Holographic Reduced Representations to enhance the generalization ability of CNNs and ViTs in the task of subitizing, addressing limitations of standard deep learning approaches from a cognitive science perspective.

Contribution

The paper proposes a novel HRR-based loss function that improves subitizing generalization in CNNs and ViTs, integrating cognitive science tools into deep learning training.

Findings

HRR loss improves subitizing generalization but does not fully solve it

ViTs perform worse than CNNs in subitizing tasks, except with HRR loss

Saliency maps and out-of-distribution tests support the effectiveness of HRR loss

Abstract

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.