SubPoE: a subgraph-induced Product-of-Experts framework for spatial multi-omics integration

Spatial multi-omics technologies jointly profile multiple molecular layers in situ, enabling integrated characterization of tissue organization and cellular states. However, many graph-based approaches remain computationally demanding because they rely on repeated message passing over global graphs, whereas naive local sampling may disrupt cell-level correspondence when multimodal features and graph topologies are not induced synchronously. Moreover, simple concatenation or fixed-weight fusion does not explicitly account for unequal uncertainty between expression-derived and spatial evidence, making the learned representations sensitive to feature corruption, technical noise and modality inconsistency.

We present SubPoE, a subgraph-induced Product-of-Experts framework for spatial multi-omics integration. SubPoE synchronously induces aligned local subgraphs from modality-specific molecular similarity graphs and a shared spatial graph, preserving molecular-similarity topology correspondence while reducing per-iteration graph complexity. Dual-topology variational graph encoders model expression-derived structure and spatial context as probabilistic experts, which are adaptively fused according to their uncertainty through a Product-of-Experts formulation. A composite self-supervised objective further improves robustness and cross-modal alignment.

Across eight public paired spatial multi-omics datasets, SubPoE achieves competitive and comparatively stable performance against existing methods. Ablation, sensitivity, robustness and efficiency experiments further support the contributions of synchronous subgraph induction and uncertainty-aware fusion.

These results establish SubPoE as an effective approach for learning topology-preserving, uncertainty-aware representations of heterogeneous spatial multi-omics data.