Irene Chang | Searcharxiv

arXiv2026

MEDALLION: Manifold Embedding Distillation and Attributions for Low-dimensional Latent InterpretatiON

Dimensionality reduction is widely used to visualize high-dimensional data and guide scientific discovery, yet interpreting which original features contribute to low-dimensional representations remains challenging, particularly for black-box methods such as t-SNE and UMAP. We introduce \textbf{MEDALLION} (Manifold Embedding Distillation and Attributions for Low-dimensional Latent InterpretatiON), a novel framework for interpreting low-dimensional embeddings through knowledge distillation and neural feature attribution. MEDALLION distills any given embedding with a neural encoder which we explain via a broad range of existing neural feature attribution methods. Through experiments on MNIST and applications in single-cell transcriptomics, we show MEDALLION provides informative feature attributions that cast additional insights into the underlying embedding and compare its performance with existing interpretability approaches.

cs.LG↗

arXiv2026

MEDAL: Manifold Embedding Distillation via Autoencoder Learning

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 approximate inverse, and a pointwise reconstruction-based measure of distortion in the manifold space. This converts static manifold embeddings into models that can be evaluated on held-out data, enabling quantitative validation including comparing different dimension reduction methods as well as hyperparameter tuning. Across multiple benchmark and scientific case studies, we show that MEDAL enables held-out validation to determine optimal manifold embeddings and hyperparameters, reveals biologically coherent regions that are difficult to preserve in two dimensional embeddings, and detects distribution shift when new samples are mapped into a fixed reference manifold. MEDAL provides a general validation wrapper to any existing dimension reduction technique that will improve the rigor and reliability of dimension reduction in scientific workflows.

stat.ML↗