Mutual Information Surprise: Rethinking Unexpectedness in Autonomous Systems

Abstract: Recent breakthroughs in autonomous experimentation have demonstrated remarkable physical capabilities, yet their cognitive control remains limited--often relying on static heuristics or classical optimization. A core limitation is the absence of a principled mechanism to detect and adapt to the unexpectedness. While traditional surprise measures--such as Shannon or Bayesian Surprise--offer momentary detection of deviation, they fail to capture whether a system is truly learning and adapting. In this work, we introduce Mutual Information Surprise (MIS), a new framework that redefines surprise not as anomaly detection, but as a signal of epistemic growth. MIS quantifies the impact of new observations on mutual information, enabling autonomous systems to reflect on their learning progression. We develop a statistical test sequence to detect meaningful shifts in estimated mutual information and propose a mutual information surprise reaction policy (MISRP) that dynamically governs system behavior through sampling adjustment and process forking. Empirical evaluations--on both synthetic domains and a dynamic pollution map estimation task--show that MISRP-governed strategies significantly outperform classical surprise-based approaches in stability, responsiveness, and predictive accuracy. By shifting surprise from reactive to reflective, MIS offers a path toward more self-aware and adaptive autonomous systems.