DELST: Dual Entailment Learning for Hyperbolic Image-Gene Pretraining in Spatial Transcriptomics

Spatial transcriptomics (ST) maps gene expression within tissue at individual spots, making it a valuable resource for multimodal representation learning. Additionally, ST inherently contains rich hierarchical information both across and within modalities. For instance, different spots exhibit varying numbers of nonzero gene expressions, corresponding to different levels of cellular activity and semantic hierarchies. However, existing methods rely on contrastive alignment of image-gene pairs, failing to accurately capture the intricate hierarchical relationships in ST data. Here, we propose DELST, the first framework to embed hyperbolic representations while modeling hierarchy for image-gene pretraining at two levels: (1) Cross-modal entailment learning, which establishes an order relationship between genes and images to enhance image representation generalization; (2) Intra-modal entailment learning, which encodes gene expression patterns as hierarchical relationships, guiding hierarchical learning across different samples at a global scale and integrating biological insights into single-modal representations. Extensive experiments on ST benchmarks annotated by pathologists demonstrate the effectiveness of our framework, achieving improved predictive performance compared to existing methods. Our code and models are available at: https://github.com/XulinChen/DELST.