Contrastive Learning (CL) has been successfully applied to classification and other downstream tasks related to concrete concepts, such as objects contained in the ImageNet dataset. No attempts seem to have been made so far in applying this promising scheme to more abstract entities. A prominent example of these could be the concept of (discrete) Quantity. CL can be frequently interpreted as a self-supervised scheme guided by some profound and ubiquitous conservation principle (e.g. conservation of identity in object classification tasks). In this introductory work we apply a suitable conservation principle to the semi-abstract concept of natural numbers by which discrete quantities can be estimated or predicted. We experimentally show, by means of a toy problem, that contrastive learning can be trained to count at a glance with high accuracy both at human as well as at super-human ranges.. We compare this with the results of a trained-to-count at a glance supervised learning (SL) neural network scheme of similar architecture. We show that both schemes exhibit similar good performance on baseline experiments, where the distributions of the training and testing stages are equal. Importantly, we demonstrate that in some generalization scenarios, where training and testing distributions differ, CL boasts more robust and much better error performance.

本文探讨了对比学习在抽象概念（如自然数）中的应用，填补了该领域的研究空白。通过引入适当的守恒原则，实验证明对比学习能够在自然数的计数任务中获得高准确度，特别是在训练和测试分布不同的情况下表现出更强的鲁棒性。此研究为未来在更抽象的任务中运用对比学习提供了新的视角和潜力。

对比学习与抽象概念：自然数的案例