Learning to Enumerate Reorganizes Magnitude Representations
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 as a tool for testing computational sufficiency, asking whether learning to estimate number is by itself enough to reorganize how a visual system weights magnitude. We trained ResNeXt-50 networks on an enumeration task (labeling the number of dots in an image, an operationalization of a functional outcome of counting) and measured representational bias by linearly decoding number versus cumulative area from penultimate-layer features, with the two dimensions decorrelated by design. Untrained networks showed a robust area bias, with area more decodable than number. Critically, networks trained to estimate number showed a reversal, with number becoming substantially more decodable than area, and this shift emerged after a single epoch of training. The effect was not a trivial consequence of training on a dimension: a matched control trained to estimate area did not produce the mirror-image effect, because enumeration training actively suppressed area information rather than merely amplifying number. Principal component analysis confirmed a reorganization of representational geometry, with numerosity becoming the dominant axis of variation (r² = 0.95) and area variance strongly reduced. These findings provide a computational proof-of-concept that learning to enumerate can restructure magnitude representations, suggesting that the perceptual primacy of number in adults may be partly a consequence, rather than a precondition, of symbolic number acquisition.
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BibTeX
@misc{aulet2026learning,
title = {{Learning to Enumerate Reorganizes Magnitude Representations}},
author = {Lauren S Aulet},
howpublished = {PsyArXiv},
year = {2026},
month = oct,
doi = {10.31234/osf.io/356xd_v4},
url = {https://osf.io/preprints/psyarxiv/356xd_v4/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning to Enumerate Reorganizes Magnitude Representations
AU - Lauren S Aulet
PY - 2026
DA - 2026/10/04
PB - PsyArXiv
DO - 10.31234/osf.io/356xd_v4
UR - https://osf.io/preprints/psyarxiv/356xd_v4/
AB - 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 as a tool for testing computational sufficiency, asking whether learning to estimate number is by itself enough to reorganize how a visual system weights magnitude. We trained ResNeXt-50 networks on an enumeration task (labeling the number of dots in an image, an operationalization of a functional outcome of counting) and measured representational bias by linearly decoding number versus cumulative area from penultimate-layer features, with the two dimensions decorrelated by design. Untrained networks showed a robust area bias, with area more decodable than number. Critically, networks trained to estimate number showed a reversal, with number becoming substantially more decodable than area, and this shift emerged after a single epoch of training. The effect was not a trivial consequence of training on a dimension: a matched control trained to estimate area did not produce the mirror-image effect, because enumeration training actively suppressed area information rather than merely amplifying number. Principal component analysis confirmed a reorganization of representational geometry, with numerosity becoming the dominant axis of variation (r² = 0.95) and area variance strongly reduced. These findings provide a computational proof-of-concept that learning to enumerate can restructure magnitude representations, suggesting that the perceptual primacy of number in adults may be partly a consequence, rather than a precondition, of symbolic number acquisition.
ER -