Fig. 5. Disentangled latent units have better diversity and one-to-one correlation with neurons compared to baselines.

a Schematic of average correlation ratio and average unit proportion scores. A good computational model for explaining responses of single neurons should allow each neuron (grey circle) to be decodable from a single latent unit (pink circle). Green lines are Lasso regression weights as in Fig. 3a. The response of each neuron should correlate strongly with the response of only one latent unit (grey bars) as measured by the average correlation ratio (higher is better). Different neurons should correlate strongly with diverse single latent units (red circles) as measured by the average unit proportion score (higher is better). b Average correlation ratio scores are significantly higher for the β-VAE than the baseline models and the AAM model (all p < 0.01; AAM p = 3.4626e–07, ICA p = 4.3804e–07, VGG (PCA) p = 2.9275e–15, PCA p = 1.8577e–15, VAE p = 5.7259e–13, AE p = 8.2339e–16, Classifier p = 7.8206e−55, VGG (raw) p = 1.4072e–26, two-sided Welsch’s t-test). Circles, average correlation ratio score per model (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. c Average unit proportion scores are significantly higher for the β-VAE than the baseline models and the AAM model (all p < 0.01; Classifier p = 4.5163e–10, AE p = 1.4289e–04, VAE p = 4.1792e–14, ICA p = 1.1129e–19, VGG (PCA) p = 1.7441e–19, PCA p = 3.5554e–19, AAM p = 1.8075e–09, VGG (raw) p = 1.2049e–08, two-sided Welsch’s t-test). Circles, average unit proportion score per model (β-VAE, n = 51; VGG (raw), n = 22; Classifier, n = 64; VAE³⁶, n = 50; AE³⁵, n = 50; VGG (PCA)³², n = 41; PCA, n = 41; ICA, n = 50; AAM³, 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.