GeneGrad: Gene-Specific Geometric Gradients for Cell Fate Prediction in Single-Cell Transcriptomics

Single-cell profiling technologies have enabled us to study complex biological systems by resolving the gene expression variation on the single-cell level. Modeling cellular dynamics and elucidating their underlying regulatory mechanisms is essential to understand developmental processes, disease progression, and aging, and is beneficial to therapeutic strategies grounded in regenerative biology. While existing computational approaches infer cellular dynamics by reconstructing vector fields, they typically rely on gene-aggregated representations and primarily recover trajectory- or tree-like structures, limiting their ability to capture fine-grained, gene-specific, and geometrically diverse patterns. Here, we introduce GeneGrad, a multi-scale geometric representation learning framework that models cellular dynamics through gene-specific gene expression gradients defined on the intrinsic cell-state manifold. By estimating local gradients for individual genes, GeneGrad captures gene-specific geometric patterns that are ignored by capturing the major variation. We validate GeneGrad on synthetic datasets with known geometric structure, demonstrating accurate gradient recovery and pattern identification. Applying GeneGrad to human induced pluripotent stem cell (iPSC) lung differentiation and hematopoietic progenitor datasets, we show that gene gradient geometry reveals early fate bias. Together, GeneGrad provides an interpretable and general framework for learning meaningful geometric representations of cellular dynamics from static single-cell data. We further extend the framework beyond single-cell transcriptomics to additional modalities, including ATAC-seq, highlighting its utility for uncovering biologically meaningful signals in complex cellular processes.