Artificial intelligence (AI) systems struggle to generalize beyond their training data and abstract general properties from the specifics of the training examples. We propose a model that reproduces the apparent human ability to come up with a number sense through unsupervised everyday experience. The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which humans acquire and develop this ability is still poorly understood. In particular, it is not known whether acquiring such a number sense is possible without supervision from a teacher. We explore this question through a model, assuming that the learner is able to pick and place small objects and will spontaneously engage in undirected manipulation. We assume that the learner's visual system will monitor the changing arrangements of objects in the scene and will learn to predict the effects of each action by comparing perception with the efferent signal of the motor system. We model perception using standard deep networks for feature extraction and classification. We find that, from learning the unrelated task of action prediction, an unexpected image representation emerges exhibiting regularities that foreshadow the perception and representation of numbers. These include distinct categories for the first few natural numbers, a strict ordering of the numbers, and a one-dimensional signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate numerosity and subitize. Remarkably, subitization and numerosity estimation extrapolate to scenes containing many objects, far beyond the three objects used during training. We conclude that important aspects of a facility with numbers and quantities may be learned without teacher supervision.

翻译：人工智能系统难以泛化到训练数据之外，也无法从训练样本的细节中抽象出一般属性。我们提出一个模型，通过无监督的日常经验重现人类明显具备的数字感知能力。理解和操作数字与数量的能力在童年时期形成，但人类获得与发展这一能力的机制至今仍知之甚少。尤其不清楚的是，在没有教师监督的情况下，这种数字感知能力是否可能习得。我们通过一个模型来探究此问题，假设学习者能够拾取和放置小物体，并自发进行无目的操作。我们假设学习者的视觉系统会监控场景中物体的变化排列，并通过对比感知与运动系统的传出信号，学习预测每个动作的效果。我们运用标准深度网络进行特征提取与分类以建模感知过程。研究发现，从预测动作这一无关任务的学习中，涌现出出人意料的图像表征，其规律性预示了数字的感知与表征。这些规律包括前几个自然数的独立类别、数字的严格顺序，以及与数量相关的一维信号。因此，我们的模型获得了估算数量与进行感数（subitizing）的能力。值得注意的是，感数与数量估算能力可以泛化到包含多个物体的场景，远超训练时使用的三个物体。我们得出结论：数字与数量处理能力的重要方面可以在无教师监督的情况下习得。