Counting Training Creates Number-Biased Representations in Deep Neural Networks

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Abstract

Human adults show a number bias in magnitude perception, weighting numerical information more heavily than continuous magnitudes like area. However, developmental research suggests this bias is not innate: young children show an area bias that reverses to a number bias only later in development. What drives this shift? Here, we use deep neural networks to test whether learning to count is sufficient to create number-biased representations. We trained ResNeXt-50 networks on a counting task (predicting the number of dots in an image) and measured representational biases using linear decoding of number versus cumulative area from network features. Untrained networks showed a robust area bias, with area more decodable than number, reflecting an architectural prior that does not privilege discrete quantity. Networks trained on ImageNet classification retained this area bias, indicating that generic visual experience is insufficient to create number-biased representations. Self-supervised models trained on naturalistic visual input showed no bias in either direction. Critically, networks trained on counting showed a dramatic reversal: number became far more decodable than area, producing a strong number bias. This bias reversed immediately after only one epoch of training. Principal component analysis revealed that counting training completely reorganized representational geometry: numerosity became the dominant axis of variation (r² = 0.95) while area was fully suppressed (r² = 0.00). These findings provide a computational proof-of-concept that learning to count can transform magnitude representations, offering a mechanistic account of how symbolic number acquisition may drive the development of number-biased cognition.

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