NEST: Nested Embedding Representation for Multiscale Clustering

Overview & Synopsis

Real-world data often exhibits cluster structure at multiple resolutions, yet existing methods typically learn a single partition or construct an explicit hierarchy. Inspired by Matryoshka Representation Learning, we introduce NEST, an unsupervised framework that encodes coarse-to-fine structure within a single embedding. NEST jointly optimizes clustering and separation across nested prefix subspaces, enabling progressively finer distinctions as embedding dimensionality increases, with rank and within-cluster regularization that keep the embedding from collapsing. Empirically, distances in the learned embedding follow the hierarchy distance more closely than those of the input, although the hierarchy is never observed during training. On synthetic hierarchies, NEST recovers multiscale structure given only the number of clusters per level. Experiments on vision, text, and single-cell data further demonstrate multiscale organization across real-world representations. By making clustering granularity an intrinsic property of the representation, NEST provides a unified approach to multiscale structure discovery.