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. 2021 Nov 9;12:6456. doi: 10.1038/s41467-021-26751-5

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© The Author(s) 2021

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. 6 — a Schematic representation of linearly accessible information overlap between the population of neurons (green) and model representation (blue) corresponding to the different combinations of magnitudes of the encoding and decoding scores. b Ratio of total neuron population (n = 159) for which single β-VAE units explain more variance than X% of variance explained by the best baseline model (AAM, 50 units). See Supplementary Fig. 3 for more details. Source data are provided as a Source Data file. c Encoding variance explained. No significant difference is found between encoding variance explained by neuron subsets and AE, ICA, VAE, PCA and AAM (β-VAE p = 2.4689e–08, AAM p = 0.1211, VGG (PCA) p = 2.5055e–07, PCA p = 0.0174, Classifier p = 2.6311e–17, ICA p = 0.0185, AE p = 0.0368, VAE p = 0.0176, VGG (raw) p = 8.4568e–18, two-sided Welsch’s t-test). Circles, median explained variance across 159 neurons (β-VAE, n = 51; VGG (raw), n = 22; Classifier, n = 64; VAE, Variational AutoEncoder³⁶, n = 50; AE, AutoEncoder³⁵, n = 50; VGG (PCA)³², n = 41; PCA, n = 41; ICA, n = 50; AAM, active appearance model³, n = 21). Boxplot centre is median, box extends to 25th and 75th percentiles, whiskers extend to the most extreme data that are not considered outliers, outliers are plotted individually. Source data are provided as a Source Data file. d Decoding variance explained. β-VAE variance explained is statistically significantly different from all other models (all p < 0.01; AAM p = 7.6510e–07, VGG (PCA) p = 0.0, PCA p = 6.0566e–23, Classifier p = 0.0, ICA p = 2.8584e–20, AE p = 0.0164, VAE p = 1.1390e–12, VGG (raw) p = 0.0, two-sided Welsch’s t-test). Circles, median explained variance across model units (β-VAE, n = 51; VGG (raw), n = 22; Classifier, n = 64; VAE, Variational AutoEncoder³⁶, n = 50; AE, AutoEncoder³⁵, n = 50; VGG (PCA)³², n = 41; PCA, n = 41; ICA, n = 50; AAM, active appearance model³, n = 21). Boxplot centre is median, box extends to 25th and 75th percentiles, whiskers extend to the most extreme data that are not considered outliers, outliers are plotted individually. Source data are provided as a Source Data file.