SpatialNP: Gridded Transformer Neural Processes for Probabilistic Spatial Proteomics in Multiplexed Tissue Imaging

Multiplexed imaging technologies such as co-detection by indexing (CODEX) and immunohistochemistry (IHC) enable simultaneous measurement of tens of protein markers at single-cell resolution across intact tissue sections, yielding spatially irregular point clouds of up to hundreds of thousands of cells. Existing spatial analysis methods either discard predictive uncertainty or scale poorly to high-dimensional multivariate outputs. To overcome these issues, we propose SpatialNP, a Gridded Transformer Neural Process that maps irregularly sampled protein observations to a continuous probabilistic spatial field over protein marker expression. A structured latent grid serves as a spatial bottleneck: context cells populate the grid via cross-attention, self-attention propagates spatial dependencies, and a second cross-attention decoder evaluates the field at arbitrary query locations, yielding per-location Gaussian predictive distributions for all markers. The latent grid further enables unsupervised tissue region discovery as features of downstream tasks like spatial clustering, cell type annotation and visualization. Experiments on structured synthetic data and real-world CODEX data demonstrate spatially coherent marker maps, well-calibrated uncertainty, and interpretable tissue region embeddings, establishing a principled probabilistic framework for spatial proteomics.