Amortized Variational Inference for Scalable Bayesian Tensor Factorization in Spatial Transcriptomics

Abstract Background: Spatial transcriptomics and single-cell RNA-sequencing (scRNA-seq) provide unprecedented insights into the spatial morphologies of latent biological pathways. While Bayesian Tensor Factorization (e.g., CANDECOMP/PARAFAC) offers a rigorous probabilistic framework to deconvolve these pathways and quantify inherent biological noise, traditional inference methods rely on local Markov Chain Monte Carlo (MCMC) or coordinate-ascent updates. The O ( N ) computational complexity of these approaches renders them intractable for modern, high-dimensional clinical datasets containing hundreds of thousands of cells. Methods: We propose a foundational proof-of-concept architecture that bridges deep learning and probabilistic graphical models via Amortized Variational Inference. By replacing iterative local parameter updates with an amortized neural encoder, we map cell-specific transcriptomic profiles directly to their latent Gaussian parameters. This decouples the parameter space from the dataset size, allowing model training to scale gracefully via stochastic mini-batch optimization, and reducing test-time inference of latent states to a highly parallelizable O (1) forward pass. Results: We validate the framework across two experimental paradigms. First, a simulation study with known continuous latent factors demonstrates strict mathematical identifiability and accurate recovery of topological structure, evidenced by a tightly bounded mean Tucker Congruence Coefficient of 0 . 96 ± 0 . 015. Second, application to a benchmark 10x Genomics Peripheral Blood Mononuclear Cell (PBMC) dataset demonstrates robust scalability and optimization stability. The convergence of the reconstruction error and KL-divergence regularization is strongly consistent with the avoidance of posterior collapse. Conclusion: Amortized inference provides a computationally viable, mathematically rigorous alternative to standard Bayesian tensor decomposition. This framework establishes a scalable, probabilistic foundation for biomarker discovery in complex spatial morphologies.