Fig. 3. Strong alignment between single neurons and disentangled units.

a Schematic of alignment score^{29, 63}. Green arrows, lasso regression weights obtained from predicting neural responses from model units (thickness indicates weight magnitude). High alignment scores are obtained when per-neuron regression weights have low entropy (one strong weight); high entropy (all incoming weights are of equal magnitude) results in low alignment scores. b β-VAE alignment scores match the ceiling provided by subsets of neurons (p = 0.4345, two-sided Welsch’s t-test). Circles, alignment per model (n = 51) or neuron subsets (n = 50). 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 Alignment scores per model (n = 51) or neuron subsets (n = 50) against artificial neural responses (linear recombination of original neural responses). 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 Alignment scores correlate with the disentanglement quality of latent units obtained from 400 β-VAE models trained with different β values (indicated by colour). UDR, Unsupervised Disentanglement Ranking³¹, measures the quality of disentanglement, higher is better. Red line, least squares fit (r = 0.96, Pearson correlation). Source data are provided as a Source Data file. e Running correlation between UDR and alignment scores across subsets of models. Models in each subset were trained with different β values, with the number of β values in each subset indicated on the x-axis. Rightmost circle, Pearson correlation across 400 β-VAE models, spanning 40 β values as reported in (d). Leftmost circle, average across 40 Pearson correlations, each calculated with 10 models with a single β value. Bars, standard deviation. Source data are provided as a Source Data file.