Energy-Regularized Graph Learning for Multiscale Spatial Representation

Spatial omics map gene and protein expression in situ , demanding methods that recover cellular and tissue architecture from noisy, high-dimensional data. This need spans two scales: (i) subcellular, where high-resolution measurements must be grouped into coherent cells, and (ii) tissue-wide, where the goal is to recover spatial domains. Existing embedding approaches either ignore space or rely on static neighborhood graphs that over- or under-smooth local heterogeneity. We present Glimmer ( G raph- L earned I nference of M ultiscale M olecular E mbedding for Spatial R epresentation), a unified framework that learns adaptive neighborhood graphs by minimizing Dirichlet energy under a log-barrier regularizer. Beginning from a k -nearest neighbor scaffold, Glimmer adaptively reweights edges to balance molecular similarity and spatial proximity, yielding interpretable, locally smoothed embeddings. These graphs enable segmentation-free reconstruction from transcript localizations or fine bins and support the discovery of tissue niches at large tissue scales. Across diverse datasets and modalities (Slide-tags, Slide-seq, MERFISH, Xenium, and CODEX), Glimmer surpasses kernel and graph neural network based methods in clustering accuracy and spatial conservation. At the subcellular level, Glimmer corrects transcript-to-cluster misassignments on lymph node slides, thereby improving gene specificity within biological clusters and addressing a key challenge in spatial transcriptomics. At the tissue-wide scale, Glimmer enables accurate region identification, as demonstrated in tonsil tissue by resolving germinal center subregions, which in turn facilitates niche-specific immune profiling. Glimmer thus offers a generalizable framework for spatial representation learning across scales and modalities, enabling comprehensive insights into tissue architecture and cellular ecosystems.