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. 2023 Jun 29;14:3843. doi: 10.1038/s41467-023-39548-5

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© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 8 — A, B Multidimensional scaling (MDS) reveals a low-dimensional representation of each input stimuli (1–9) in a two-dimensional space. The two-dimensional representations of each input at each epoch were obtained from multiple groups of neurons, using (a) the whole layer, (b) P-SPONs based on selective numerosity neurons, (c) New+Switch based on selective numerosity neurons, (d) P-SPONs based on all numerosity neurons, and (e) New+Switch based on all numerosity neurons, for A pre-trained and B post-training networks. The two-dimensional representations are color coded by layer (V1: light blue, V2: green, V3: red, IPS: dark blue). The MDS reveals the emergence of a clear two-dimensional arch structure in V3 and especially in IPS, post numerosity training. This structure is not present for the pre-trained network. This representation also shows that whilst whole layer representations depend on SPONs pre-training (compare Aa and Ad), they shift to newly trained and switched neurons post training (compare Ba and Be), as well as the fact that they depend not just on the selective numerosity neurons (b, c) but on all numerosity neurons including those sensitive to both numerosity and condition (d, e). C–G The two dimensions obtained from the MDS using (C) all neurons, (D) P-SPONs based on selective numerosity neurons, (E) New+Switch based on selective numerosity neurons, (F) P-SPONs based on all numerosity neurons, and (G) New+Switch based on all numerosity neurons, are evaluated for covariance with key input stimulus properties. These include the stimulus magnitude (perceptual property), and distance of the input from the mid-point of the stimuli space (cognitive property). Across these sets the pre-training covariances are low, but post-training covariance between (a) dimension 1 and magnitude, and between (d) dimension 2 and distance from mid-point of the stimuli space, increase post-training in the IPS layer, especially in (A) and (G). The covariance between (b) dimension 2 and magnitude, and (c) dimension 1 and distance from mid-point remain low post-training. Source data are provided as a Source Data file.