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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. 7 — A, B Neural representation similarity (NRS) calculated based on pairwise similarity between the mean activation across neurons in each layer (a) V1, (b) V2, (c) V3, and (d) IPS, for each value of the input stimuli. This shows us how well differentiated each input stimuli are, compared to other input values, in terms of their neuronal representations, pre-training (A) and post-training (B). The influence of training in the whole layer level RSA can be seen strongly in IPS, to a progressively smaller extent in V3 and negligible in V2 and V1. C, D The NRS is condensed to map the dissimilarity (1- average NRS) averaged as a function of each unique value of difference between inputs, that is, directly measure the numerical distance effect between representations of numerosities at a distributed level. A robust representation should show a sharply increasing linear trend in the average similarity with increasing input difference. The condensed RSA as a function of input difference is calculated for (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. Pre-training (C), these linear trends have a very small slope. This slope increases with numerosity training (D), with significantly larger increases as we move from lower to higher layers, especially in IPS. E, F The NRS is condensed to map the dissimilarity (1- average NRS) averaged as a function of each unique value of $\log$ -ratio between inputs, that is, directly measure the ratio effect between representations of numerosities at a distributed level. This is shown for (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. A robust representation should show a sharply increasing linear trend in the average similarity with increasing $\log$ -ratio. Source data are provided as a Source Data file.