A Hierarchical Sheaf Spectral Embedding Framework for Single-Cell RNA-seq Analysis

Single-cell RNA-seq representation learning is fundamentally label-free: cell identities, states, and contexts are not fixed training targets, so what constitutes signal or nuisance is analysis-dependent. A single representation must therefore preserve biological identity and state, remain robust to nuisance context, and retain the gene-level variation needed for expression analysis, three demands we call the representation trilemma. To tackle this problem, we introduce scTrilemma, a latent-bottleneck VAE that routes expression-derived variation to the embedding, the decoder, or the prior rather than forcing all of it through one embedding. It gates gene tokens by expression, routes the cell representation through the decoder, and conditions the prior on unlabeled pseudo-bulk context, under a single reconstruction objective and without target annotations or auxiliary representation losses. In release-based zero-shot evaluation on successive CZ CELLxGENE Census releases, scTrilemma leads all three demands at once and preserves biological-state, differential-expression, and pathway structure across multiple disease settings. Latent interventions further show that context can be removed at almost no cost to the other demands, leaving identity against fidelity as the remaining tension. Code is publicly available at https://github.com/yunhak0/scTrilemma.

Single-cell transcriptomics enables profiling of cellular states at unprecedented resolution, but its high dimensionality, sparsity, and technical batch effects pose significant challenges for representation learning. Existing single-cell foundation models typically encode each cell independently or only model cells from the same batch for denoising, thereby underutilizing the rich relational information across batches and cell types to model gene expression patterns. We argue that single-cell models can benefit from more informative cell-context modeling. By comparing consistency and variation across cells, models can capture fine-grained gene-gene dependencies associated with cell states, which are essential for learning high-quality representations. Inspired by the use of multiple sequence alignment (MSA) context in protein modeling, we propose CellMSA, a single-cell representation learning framework that introduces an MSA-inspired inductive bias into transcriptomic modeling. For each target cell, CellMSA retrieves relevant cells from different batches and biologically related cell types as context, and summarizes cross-cell patterns into a context-dependent gene-pair representation. This representation is then injected into a pair-aware target-cell encoder for fine-grained representation learning. We pretrain CellMSA on a large-scale human single-cell corpus of approximately 109 million cell observations, including 65.6 million primary observations. Experiments show that our framework consistently outperforms existing methods across multiple benchmarks. Code is available at the following repository: https://github.com/PharMolix/CellMSA.

Single-cell RNA sequencing (scRNA-seq) data exhibit strong and reproducible statistical structure. This has motivated the development of large-scale foundation models, such as TranscriptFormer, that use transformer-based architectures to learn a generative model for gene expression by embedding genes into a latent vector space. These embeddings have been used to obtain state-of-the-art (SOTA) performance on downstream tasks such as cell-type classification, disease-state prediction, and cross-species learning. Here, we ask whether similar performance can be achieved without utilizing computationally intensive deep learning-based representations. Using simple, interpretable pipelines that rely on careful normalization and linear methods, we obtain SOTA or near SOTA performance across multiple benchmarks commonly used to evaluate single-cell foundation models, including outperforming foundation models on out-of-distribution tasks involving novel cell types and organisms absent from the training data. Our findings highlight the need for rigorous benchmarking and suggest that the biology of cell identity can be captured by simple linear representations of single cell gene expression data.