Neural Bayesian Sequential Routing

• URL: http://arxiv.org/abs/2605.26147v1
• Date: Fri, 22 May 2026 22:45:56 GMT
• Title: Neural Bayesian Sequential Routing
• Abstract summary: We introduce textbfNeural Bayesian Sequential Routing (NBSR), a framework that models neural inference as active evidence accumulation over a hierarchical Directed Acyclic Graph (DAG)<n>NBSR achieves competitive predictive performance while providing transparent routing traces, path-dependent evidence attribution, uncertainty-aware decision control, and resource-rational inference.<n>Overall, NBSR offers a mathematically grounded framework for interpretable, modular, and resource-rational agentic AI.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Human decision-making is sequential and uncertainty-aware, yet standard neural networks often rely on static, dense forward computation with limited visibility into evidence acquisition, uncertainty evolution, or when computation should stop. We introduce \textbf{Neural Bayesian Sequential Routing (NBSR)}, a framework that models neural inference as active evidence accumulation over a hierarchical Directed Acyclic Graph (DAG). Within a Dirichlet--Categorical conjugate framework, neural experts query a persistent global knowledge oracle to extract positive evidence vectors, which act as pseudo-counts and update a Dirichlet belief state by exact conjugate addition. Coupled with a Gumbel-Softmax Straight-Through estimator, this update enables hard, path-dependent routing while preserving surrogate gradients for end-to-end training. The resulting Dirichlet precision and entropy provide mechanisms for uncertainty quantification, entropy-based early exiting, OOD abstention, and cost-aware evidence acquisition. We prove that, under strictly positive evidence extraction, total Dirichlet precision increases monotonically along any valid trajectory and marginal predictive variance is bounded, formalizing sequential ``hypothesis sharpening''; under idealized capacity and optimization assumptions, the terminal Dirichlet expectation recovers the Bayes-optimal conditional distribution. Empirical evaluations across visual categorization, structured medical diagnosis, language modeling, partially observable control, and cost-aware Bayesian experimental design show that NBSR achieves competitive predictive performance while providing transparent routing traces, path-dependent evidence attribution, uncertainty-aware decision control, and resource-rational inference. Overall, NBSR offers a mathematically grounded framework for interpretable, modular, and resource-rational agentic AI.

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