Theoretical Foundations of Latent Posterior Factors: Formal Guarantees for Multi-Evidence Reasoning

Computer Science > Artificial Intelligence [Submitted on 13 Mar 2026] Theoretical Foundations of Latent Posterior Factors: Formal Guarantees for Multi-Evidence Reasoning Aliyu Agboola Alege We present a complete theoretical characterization of Latent Posterior Factors (LPF), a principled framework for aggregating multiple heterogeneous evidence items in probabilistic prediction tasks. Multi-evidence reasoning arises pervasively in high-stakes domains including healthcare diagnosis, financial risk assessment, legal case analysis, and regulatory compliance, yet existing approaches either lack formal guarantees or fail to handle multi-evidence scenarios architecturally. LPF encodes each evidence item into a Gaussian latent posterior via a variational autoencoder, converting posteriors to soft factors through Monte Carlo marginalization, and aggregating factors via exact Sum-Product Network inference (LPF-SPN) or a learned neural aggregator (LPF-Learned). We prove seven formal guarantees spanning the key desiderata for trustworthy AI: Calibration Preservation (ECE <= epsilon + C/sqrt(K_eff)); Monte Carlo Error decaying as O(1/sqrt(M)); a non-vacuous PAC-Bayes bound with train-test gap of 0.0085 at N=4200; operation within 1.12x of the information-theoretic lower bound; graceful degradation as O(epsilon*delta*sqrt(K)) under corruption, maintaining 88% performance with half of evidence adversarially replaced; O(1/sqrt(K)) calibration decay with R^2=0.849; and exact epistemic-aleatoric uncertainty decomposition with error below 0.002%. All theorems are empirically validated on controlled datasets spanning up to 4,200 training examples. Our theoretical framework establishes LPF as a foundation for trustworthy multi-evidence AI in safety-critical applications. Comments: 30 pages, 8 figures, 10 tables. Theoretical characterization of the Latent Posterior Factors (LPF) framework for multi-evidence probabilistic reasoning, with formal guarantees and empirical validation Subjects: Artificial Intelligence (cs.AI); Information Theory (cs.IT); Machine Learning (cs.LG); Machine Learning (stat.ML) MSC classes: 68T37 (Primary), 68T05, 62F15, 62G15 ACM classes: I.2.6; I.2.4; G.3; I.2.3 Cite as: arXiv:2603.15674 [cs.AI]   (or arXiv:2603.15674v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.15674 Focus to learn more Submission history From: Aliyu Alege [view email] [v1] Fri, 13 Mar 2026 17:44:14 UTC (166 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT cs.LG math math.IT stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)