This question is explored through a model, where a pre-trained motor system is teaching perception. The assumption is that the learner is able to pick and place small objects and will spontaneously engage in undirected manipulation, e.g. playing with small objects. Further assumptions are 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. Perception is modelled using standard deep networks for feature extraction and classification, and gradient descent learning.
The main finding is that, from learning the unrelated task of action prediction, an unexpected image representation emerges exhibiting regularities that foreshadow the perception and (I will of numbers and quantities. These include distinct categories for zero and the first few natural numbers, a strict ordering of the numbers, and a one-dimensional signal that correlates with numerical quantity. As a result, the model acquires the ability to estimate numerosity, i.e. the number of objects in the scene, as well as subitization, i.e. the ability to recognize at a glance the exact number of objects in small scenes. Remarkably, subitization and numerosity estimation extrapolate to scenes containing many objects, far beyond the three objects used during training.
The conclusion is that important aspects of a facility with numbers and quantities may be learned without teacher supervision.
Literature:
Neehar Kondapaneni, Pietro Perona. A Number Sense as an Emergent Property of the Manipulating Brain, arXiv:2012.04132, 2020 – https://arxiv.org/abs/2012.04132