In the spirit of Turing test, we design and conduct a set of visual numerosity experiments with deep neural networks. We train DCNNs with a large number of sample images that are varied visual representations of small natural numbers, towards the objective of learning numerosity perception. Numerosity perception, or the number sense, is a cognitive construct so primary and so critical to the survival and well-being of our species that is considered and proven to be innate to human infants, and it responds to visual stimuli prior to the development of any symbolic skills, language or arithmetic. Somewhat surprisingly, in our experiments, even with strong supervision, DCNNs cannot see through superficial variations in visual representations and distill the abstract notion of natural number, a task that children perform with high accuracy and confidence. DCNNs are apparently easy to be confused by geometric variations and fail to grasp the topological essence in numerosity. The failures of DCNNs in the proposed cognition experiments also expose their overreliance on sample statistics at the expense of image semantics. Our findings are, we believe, significant and thought-provoking in the interests of AI research, because visual-based numerosity is a benchmark of minimum sort for human intelligence.

本文考察了深度学习在学习数字及subitizing任务上的表现，发现基于样例的深度学习模型无法抽象数字的本质特征；作者构建了一种能够进行subitizing的循环神经网络，探究使用人类洞见补充纯深度学习的方法。这一研究意义重大，因为视觉数量意识代表了人类智力的最低水平。

深度学习在数量认知方面的认知缺陷