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

arXiv: https://arxiv.org/abs/2312.15310 · HTML: https://mlsanity.com/paper/2312.15310/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 23 Dec 2023.

## Builds on (most cited first, 21 of 21)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Teaching CLIP to Count to Ten](https://mlsanity.com/paper/2302.12066/) (2023)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [Bongard-LOGO: A New Benchmark for Human-Level Concept Learning and Reasoning](https://mlsanity.com/paper/2010.00763/) (2020)
- [Counting Everyday Objects in Everyday Scenes](https://mlsanity.com/paper/1604.03505/) (2016)
- [Learning to Reason with Third-Order Tensor Products](https://mlsanity.com/paper/1811.12143/) (2018)
- [Revisiting Salient Object Detection: Simultaneous Detection, Ranking, and Subitizing of Multiple Salient Objects](https://mlsanity.com/paper/1803.05082/) (2018)
- [Learning with Holographic Reduced Representations](https://mlsanity.com/paper/2109.02157/) (2021)
- [Representing Objects, Relations, and Sequences](https://mlsanity.com/paper/1501.07627/) (2015)
- [Recasting Self-Attention with Holographic Reduced Representations](https://mlsanity.com/paper/2305.19534/) (2023)
- [MIMONets: Multiple-Input-Multiple-Output Neural Networks Exploiting Computation in Superposition](https://mlsanity.com/paper/2312.02829/) (2023)
- [Salient Object Subitizing](https://mlsanity.com/paper/1607.07525/) (2016)
- [Deploying Convolutional Networks on Untrusted Platforms Using 2D Holographic Reduced Representations](https://mlsanity.com/paper/2206.05893/) (2022)
- [Cognitive Deficit of Deep Learning in Numerosity](https://mlsanity.com/paper/1802.05160/) (2018)
- [Lempel-Ziv Networks](https://mlsanity.com/paper/2211.13250/) (2022)
- [Subitizing with Variational Autoencoders](https://mlsanity.com/paper/1808.00257/) (2018)
- [A Deep Neural Network for Finger Counting and Numerosity Estimation](https://mlsanity.com/paper/1907.05270/) (2019)

## Built on by (most cited first, 4 of 4)

- [Holographic Global Convolutional Networks for Long-Range Prediction Tasks in Malware Detection](https://mlsanity.com/paper/2403.17978/) (2024)
- [A Walsh Hadamard Derived Linear Vector Symbolic Architecture](https://mlsanity.com/paper/2410.22669/) (2024)
- [A Vector Symbolic Approach to Multiple Instance Learning](https://mlsanity.com/paper/2511.16795/) (2025)
- [Disentanglement with Holographic Reduced Representations](https://mlsanity.com/paper/2606.09725/) (2026)

## Abstract (arXiv)

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.