Learning exact enumeration and approximate estimation in deep neural network models

• Main Authors: Creatore, C. (Author), Sabathiel, S. (Author), Solstad, T. (Author)
• Format: Article
• Language: English
• Published: Elsevier B.V. 2021
• Subjects: Approximate number; Computational modelling; Deep neural networks; Exact number; human; Humans; learning; Learning; Neural Networks, Computer; Number sense; Representations
• Online Access: View Fulltext in Publisher

 A system for approximate number discrimination has been shown to arise in at least two types of hierarchical neural network models—a generative Deep Belief Network (DBN) and a Hierarchical Convolutional Neural Network (HCNN) trained to classify natural objects. Here, we investigate whether the same two network architectures can learn to recognise exact numerosity. A clear difference in performance could be traced to the specificity of the unit responses that emerged in the last hidden layer of each network. In the DBN, the emergence of a layer of monotonic ‘summation units’ was sufficient to produce classification behaviour consistent with the behavioural signature of the approximate number system. In the HCNN, a layer of units uniquely tuned to the transition between particular numerosities effectively encoded a thermometer-like ‘numerosity code’ that ensured near-perfect classification accuracy. The results support the notion that parallel pattern-recognition mechanisms may give rise to exact and approximate number concepts, both of which may contribute to the learning of symbolic numbers and arithmetic. © 2021 The Author(s)