Extended Data Fig. 5 ∣. Effect of latent space dimensionality on reconstruction performance.

errors for coupled autoencoder and linear baseline for different latent space dimensionality dim ∈ {3, 5, 10}. Coupled autoencoders reconstruct the data more accurately than linear baselines (p < 10⁻⁴, two-sided Wilcoxon signed-rank test). The only exception is for $X_{\mathrm{t}}\to {\tilde{X}}_{\mathrm{e}}$ with dimensionality set to 10, where the null hypothesis cannot be rejected. We would like the dimensionality to be as low as possible for downstream tasks such as clustering and classification with limited data, and as high enough for good performance at tasks such as data imputation or cross-modal data prediction.