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This paper introduces Latent Posterior Factors (LPF), a framework that leverages VAE latent posteriors as soft likelihood factors for Sum-Product Network (SPN) inference, enabling probabilistic reasoning over unstructured evidence with calibrated uncertainty. LPF is instantiated in two architectures: LPF-SPN (structured factor-based inference) and LPF-Learned (end-to-end learned aggregation) to compare probabilistic reasoning and learned aggregation. Experiments across eight domains show LPF-SPN achieves high accuracy (up to 97.8%) and low calibration error (ECE 1.4%), outperforming evidential deep learning, LLMs, and graph-based baselines.
Achieve 97.8% accuracy and 1.4% calibration error in multi-evidence reasoning by fusing VAE latent uncertainty with Sum-Product Networks, outperforming LLMs and other baselines.
Real-world decision-making, from tax compliance assessment to medical diagnosis, requires aggregating multiple noisy and potentially contradictory evidence sources. Existing approaches either lack explicit uncertainty quantification (neural aggregation methods) or rely on manually engineered discrete predicates (probabilistic logic frameworks), limiting scalability to unstructured data. We introduce Latent Posterior Factors (LPF), a framework that transforms Variational Autoencoder (VAE) latent posteriors into soft likelihood factors for Sum-Product Network (SPN) inference, enabling tractable probabilistic reasoning over unstructured evidence while preserving calibrated uncertainty estimates. We instantiate LPF as LPF-SPN (structured factor-based inference) and LPF-Learned (end-to-end learned aggregation), enabling a principled comparison between explicit probabilistic reasoning and learned aggregation under a shared uncertainty representation. Across eight domains (seven synthetic and the FEVER benchmark), LPF-SPN achieves high accuracy (up to 97.8%), low calibration error (ECE 1.4%), and strong probabilistic fit, substantially outperforming evidential deep learning, LLMs and graph-based baselines over 15 random seeds. Contributions: (1) A framework bridging latent uncertainty representations with structured probabilistic reasoning. (2) Dual architectures enabling controlled comparison of reasoning paradigms. (3) Reproducible training methodology with seed selection. (4) Evaluation against EDL, BERT, R-GCN, and large language model baselines. (5) Cross-domain validation. (6) Formal guarantees in a companion paper.