Neural Bayesian Sequential Routing

2026-05-22

AI Summary

This work addresses the limitations of standard neural networks in reasoning—specifically their inability to quantify uncertainty, dynamically accumulate evidence, and decide when to terminate computation. The authors model neural inference as an active evidence accumulation process over a hierarchical directed acyclic graph, leveraging a Dirichlet–Categorical conjugate framework to enable path-dependent hard routing and precise belief state updates. A provable “hypothesis sharpening” mechanism is introduced, endowing the system with capabilities for uncertainty quantification, entropy-driven early stopping, out-of-distribution rejection, and resource-rational reasoning, while recovering Bayes-optimal predictions under ideal conditions. Experiments demonstrate competitive performance across visual classification, medical diagnosis, and language modeling tasks, alongside interpretable routing trajectories, path-dependent evidence attribution, and adaptive computation.

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.

Problem

• sequential decision-making
• uncertainty quantification
• evidence accumulation
• early exiting
• Bayesian inference

Innovation

• Neural Bayesian Sequential Routing
• Dirichlet-Categorical conjugacy
• evidence accumulation
• uncertainty-aware routing
• resource-rational inference