Fig. 4. Disentangled latent units align with single neurons better than baselines.

a Alignment scores are significantly higher for the β-VAE than the baseline models and the “gold standard” provided by the AAM (all p < 0.01, two-sided Welsch’s t-test; VGG (raw) p = 7.4220e–06, Classifier p = 0.0, AAM p = 9.1757e–42, VAE p = 9.7811e–43, VGG (PCA) p = 1.9383e–35, PCA p = 0.0, AE p = 0.0, ICA p = 0.0). Circles, alignment 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). Red circle indicates VGG (raw) with all N = 4096 units from the last hidden layer. Teal boxplot—random baseline with sparseness matched to the 51 β-VAE models. 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. b Per-neuron alignment scores. Scores are discretised into equally spaced bins. Scores in each row are arranged in descending order. The results from single models, chosen to have the median alignment score. VGG (raw) results are presented from the model that contained all N = 4096 units from the last hidden layer. Arrows point to neurons from Fig. 2b within the β-VAE alignment scores. Source data are provided as a Source Data file.