Laminar: Querying Biology at Any Scale with Tissue Embedding Fields

Biology is organized at nested spatial scales, from molecules to cells to multicellular neighborhoods, whose functions emerge from multi-scale organizations rather than any single cell. Imaging-based spatial transcriptomics (iST) captures all of these scales in a single experiment, measuring up to billions of individual transcripts, each with its gene identity and sub-micrometer position. To handle this volume, existing foundation models pool transcripts into predefined units such as cells, patches, or bins before learning, which fixes the representation to a single spatial scale and discards the molecular geometry within each unit. We introduce *tissue embedding fields*, a representation that assigns contextual embeddings on a shared unit hypersphere to every measured transcript. A region of any size or shape, from a single cell to a whole section, can then be represented by summing and normalizing the embeddings of the transcripts it contains, without re-encoding the tissue. The spatial unit of analysis is therefore chosen at query time rather than fixed during training. To compute such fields at billion-transcript scale, we introduce Laminar, a local-to-global encoder whose cost grows linearly with transcript count. A graph neural network exchanges short-range molecular information over local transcript graphs while a quadtree spatial Transformer propagates information to progressively larger tissue tiles. Each transcript then retrieves this multi-scale context through cross-attention, yielding its final embedding. We train Laminar using a joint-embedding predictive architecture, where a context encoder processes spatially- and gene-masked tissue, while a predictor matches multi-scale regional representations of the complete tissue. A single Laminar encoder pretrained on 632 public human iST sections, evaluated frozen on eight transfer tasks spanning cell, niche, and tissue scales, achieves the best scores on tissue-scale tasks while remaining competitive with fixed-scale foundation models at cell scale, with an overall best mean rank. Laminar shows that biological representations need not be tied to predefined spatial units; a unified representation enables reasoning across the hierarchy of tissue organization.