MEDAL: Manifold Embedding Distillation via Autoencoder Learning
arXiv:2605.24244v1 Announce Type: cross Abstract: Low-dimensional embeddings are widely used as visual summaries of high-dimensional data and to enable downstream scientific discoveries. Yet, popular nonlinear dimension reduction methods, such as t-SNE and UMAP, are often selected based on visual appeal alone and without rigorous quantitative validation. A major reason is that manifold embeddings typically do not provide an out-of-sample map nor an inverse back to the original feature space; this makes held-out validation, the gold standard in supervised learning, all but impossible. To address these challenges, we develop a novel framework, MEDAL (Manifold Embedding Distillation via Autoencoder Learning), which distills a fitted manifold embedding into a reusable encoder--decoder model. MEDAL trains a constrained autoencoder whose bottleneck exactly matches any teacher embedding while the decoder reconstructs the original input; this yields an explicit map for new samples, an approxim