The Bayesian Reflex: Online Learning as the Autonomic Nervous System of Modern and Future AI

TL;DR

The paper introduces the Bayesian reflex as a unifying framework for online learning in AI, emphasizing probabilistic belief maintenance, sequential updating, and uncertainty-driven decision-making inspired by the autonomic nervous system.

Contribution

It presents a comprehensive framework for adaptive online Bayesian methods, including computational principles and applications across diverse dynamic models and decision processes.

Findings

Survey of online Bayesian methods and computational principles.

Application to climate dynamics, prime number discovery, and point process characterization.

Extension to assess convergence and model complex phenomena like the Riemann Hypothesis.

Abstract

This chapter introduces the Bayesian reflex -- an analogy with the autonomic nervous system -- as a unifying framework for online learning in AI. Bayesian online algorithms automatically maintain equilibrium in dynamic environments via three mechanisms: belief maintenance through probabilistic representations, sequential updating via Bayes' theorem, and uncertainty-driven action balancing exploration and exploitation. We survey online Bayesian methods, highlighting two computational principles: the look-up table principle for sequential inference in function space, and the ellipsoidal decomposition framework for nearly exact i.i.d. sampling from arbitrary posteriors. These principles are generalized across dynamic emulation, nonparametric state-space models, circular time series, inverse regression for climate model evaluation, and deep architectures via Recursive Gaussian Processes. Decision-making is explored via Thompson sampling and restless bandits. We extend the framework to assess infinite series convergence (applied to climate dynamics and the Riemann Hypothesis), model prime number distributions leading to the discovery of 184 strong Mersenne prime candidates, detect stationarity, and characterize point processes. The Bayesian reflex provides a foundational infrastructure for adaptive AI that continuously learns in a complex world.