The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which this ability is developed is still poorly understood. In particular, it is not known whether acquiring such a {\em number sense} is possible without supervision from a teacher. To explore this question, we propose a model in which spontaneous and undirected manipulation of small objects trains perception to predict the resulting scene changes. We find that, from this task, an image representation emerges that exhibits regularities that foreshadow numbers and quantity. These include distinct categories for zero and the first few natural numbers, a notion of order, and a signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate the number of objects in the scene, as well as {\em subitization}, i.e. the ability to recognize at a glance the exact number of objects in small scenes. We conclude that important aspects of a facility with numbers and quantities may be learned without explicit teacher supervision.

翻译：理解和操控数字和数量的能力在童年时期就出现了,但是发展这种能力的机制仍然不易理解。 特别是,不知道在没有教师监督的情况下能否获得这样一个 ~em编号感官。 为探讨这一问题,我们提出了一个模式,让小物体的自发和非定向操控能够使感知到随之而来的场景变化。我们发现,从这一任务中,图像显示的规律性呈现出预示数字和数量。其中包括零和前几个自然数字的不同类别、秩序概念和与数量相关的信号。结果,我们的模型获得估计现场物体数量以及子化功能的能力,即能够一目即辨别小场景中物体的确切数量。我们的结论是,一个具有数量和数量的设施的重要方面可以在没有明确教师监督的情况下学习。