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

arXiv stat.ML / 5/5/2026

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Key Points

The paper proposes the “Bayesian reflex,” a conceptual framework likening Bayesian online learning to the autonomic nervous system for maintaining stability in changing AI environments.
It argues that Bayesian online algorithms achieve equilibrium through belief maintenance with probabilistic representations, sequential Bayesian updating, and uncertainty-driven trade-offs between exploration and exploitation.
The chapter surveys key computational ideas such as the look-up table principle for sequential inference in function space and an ellipsoidal decomposition approach for nearly exact i.i.d. sampling from arbitrary posteriors.
It demonstrates how the framework generalizes across diverse domains and models, including dynamic emulation, nonparametric state-space models, circular time series, climate-model inverse regression, and deep architectures via Recursive Gaussian Processes.
It extends the decision and inference perspective to methods like Thompson sampling and restless bandits, and discusses applications ranging from infinite-series convergence and stationarity detection to prime-number distributions and point-process characterization.

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.