SubPoE addresses two computational problems encountered in spatial multi-omics analysis. First, many graph-based methods repeatedly transmit information across an entire global graph, which can require substantial computation and memory as the number of spatial observations grows. Second, they may combine molecular-similarity and spatial evidence with fixed weights even when the two sources carry different levels of uncertainty for an individual cell or spot. The new method extracts aligned local subgraphs during training and represents molecular and spatial information as probabilistic “experts.” Their contributions are combined according to their estimated precision, allowing a more certain source to exert greater influence on the final latent representation. The overall design seeks to preserve cell-level correspondence while making the model less dependent on a single molecular feature or modality.

At the start of each training iteration, SubPoE resamples seed observations and expands them through a precomputed neighborhood graph until a target-sized local node set is formed. The same active observations are then used to extract aligned features and edges from every modality-specific molecular-similarity graph and from one shared spatial graph. Molecular graphs are built by retaining observations with the strongest Pearson-correlation relationships within each molecular modality, while the spatial graph uses nearest neighbors defined by Euclidean distance between tissue coordinates. Because the node set and features are synchronized across these topologies, a given cell or spatial spot remains the same unit throughout graph construction, encoding and reconstruction. The induced edges are reindexed into a common local coordinate system before processing, avoiding the loss of correspondence that can occur when modalities are sampled independently.

Each molecular modality is encoded through two variational graph branches. One operates on the induced molecular-similarity topology and captures feature-derived cellular relationships; the other augments that topology with spatial connections and represents neighborhood context. Rather than concatenating or averaging their outputs, SubPoE treats the two branches as Gaussian experts. Their posterior means and variances are fused with a Product-of-Experts formulation, in which variance is converted into precision. An expert with lower posterior uncertainty therefore contributes more strongly for that observation. This procedure is performed within each modality, producing a fused modality-specific embedding that is subsequently concatenated into the joint multi-omics representation. The authors note that this is not a fully probabilistic fusion across different molecular modalities: the final cross-modal representation still relies on concatenation, with probabilistic fusion applied to the two topology branches inside each modality.

Training is self-supervised and combines several types of constraint. Random feature masks create perturbed views while preserving observation identities and graph structures. Shared decoders reconstruct the original measurements, while cross-modal reconstruction paths ask one modality’s representation to predict another. A self-reconstruction loss combines mean squared error with Pearson-correlation distance, and additional terms regularize the variational posteriors toward a standard Gaussian and align cell-matched latent representations from different modalities. A warm-up factor is applied to the divergence term during early training to reduce the risk of posterior collapse. Together, these objectives encourage the embeddings to retain modality-specific information, support cross-modal predictability and avoid depending excessively on individual feature entries. The study evaluated the resulting representation primarily through spatial-domain identification, rather than testing a broad panel of downstream biological analyses.

Component ablations indicated that the main mechanisms made complementary contributions. On the human placenta dataset, removing node-induced subgraph sampling lowered the adjusted Rand index from 0.56 to 0.19, while replacing uncertainty-aware fusion with direct concatenation reduced it to 0.22. On human lymph-node section 1, removing subgraph sampling lowered the same score from 0.27 to 0.13, and removing feature masking reduced it to 0.14. Similar decreases were observed across the remaining datasets, and the full model generally performed best. Hyperparameter analysis showed that most settings were relatively stable across broad ranges, although subgraph size had the strongest and most tissue-dependent effect. Human placenta generally performed better with smaller subgraphs, whereas mouse brain E15 achieved its highest adjusted Rand index at an intermediate size. The authors therefore described local context size as a balance among neighborhood coverage, stochastic regularization and tissue-specific structure rather than a universal setting.

Cell-level uncertainty analysis on human tonsil section 1 showed that most observations had low posterior uncertainty in both branches, although localized hotspots were present. The estimated contribution of the spatial expert varied across the tissue, consistent with observation-specific rather than globally fixed weighting. Relative uncertainty in the spatial branch was strongly negatively associated with its contribution, directly illustrating the precision-based decision rule. That association was interpreted as a visualization of how the mechanism operates, not independent proof of improved performance; the evidence for practical benefit came from the ablation showing lower scores when Product-of-Experts fusion was replaced by concatenation. The uncertainty analysis also exposed an important boundary: it demonstrated adaptive weighting and its relationship to model confidence, but it did not establish that either branch was biologically correct in every tissue region.

Controlled perturbation experiments on mouse brain E13 tested the model’s response to corruption of the chromatin-accessibility modality. These experiments retained all matched locations and both RNA and ATAC measurements, so they assessed feature-level damage rather than the complete loss of a modality. Without retraining, the method remained stable under moderate Gaussian noise and feature dropout. At the strongest noise level, it retained 71.8% of baseline adjusted Rand index, 62.5% of normalized mutual information and 93.4% of the Fowlkes–Mallows index, while expert uncertainty increased. With 30% ATAC feature dropout, normalized mutual information retention was 94.2%, while adjusted Rand index and Fowlkes–Mallows retention remained above baseline. Scaling ATAC signals to 60% of their original magnitude produced limited deterioration, with 94.4% normalized mutual information retention. These controlled tests support tolerance of moderate perturbations, but they do not imply robustness to missing modalities or arbitrary forms of corruption.

Subgraph induction also produced computational savings while improving representation learning in the reported comparisons. On the human placenta dataset, a 256-node subgraph setting achieved an adjusted Rand index of 0.483, normalized mutual information of 0.695 and Fowlkes–Mallows index of 0.570; the corresponding full-graph scores were 0.195, 0.357 and 0.315. This pattern suggests that repeatedly resampling local neighborhoods may act partly as a regularizer, not merely as a shortcut for reducing work. Comparative profiling found that a 1,024-node setting retained about 24% of local neighbors while reducing induced edges by approximately 94%, per-step training time by 89% and batch-tensor memory by 78% relative to full-graph training. The study remains limited by its focus on paired spatial clustering tasks, its use of eight public datasets and its reliance on latent concatenation for cross-modal integration. The authors identify broader modality combinations, incomplete data, larger tissues, fully probabilistic cross-modal fusion and incorporation of biological priors as future directions.

Subject of Research: Computational integration of paired spatial RNA and chromatin or protein measurements for spatial-domain clustering

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

Article References: Li, Y., Gao, W., Ren, J., Wei, Q., Wang, X., Zhang, L., Li, R., Wang, Y., & Zhang, X. (2026). SubPoE: a subgraph-induced Product-of-Experts framework for spatial multi-omics integration. Frontiers in Genetics, 17, Article 1977260. https://doi.org/10.3389/fgene.2026.1977260

Image Credits: AI Generated

DOI: 10.3389/fgene.2026.1977260

Keywords: spatial multi-omics, spatial clustering, SubPoE, Product-of-Experts, graph neural networks, uncertainty-aware fusion, subgraph learning, spatial transcriptomics, chromatin accessibility, antibody-derived tags, subgraph-induced, framework