Latent Space Alignment

Latent space alignment studies how to make representations from different models, modalities, domains, or people comparable and useful together. Common approaches learn linear or orthogonal maps with Procrustes methods, use optimal transport or shared semantic anchors, or regularize representations to preserve geometry and task-relevant structure. These methods support tasks such as model stitching, cross-modal retrieval, domain adaptation, and cross-subject brain decoding, evaluated through measures including retrieval accuracy, activation reconstruction, and downstream task performance. A central tension is that geometric or distributional similarity does not guarantee functional compatibility: alignment can preserve nuisance information, depend on paired examples, or improve a similarity metric without improving the task.