Three Conjectures on Unexpectedeness
This work addresses foundational questions in cognitive theory for researchers, but it is incremental as it builds on existing experimental confirmations without presenting new empirical results.
The paper tackles the theoretical basis of unexpectedness in Simplicity Theory by proposing three conjectures that frame it as a generalization of Bayes' rule, link it to tracking ergodic properties, and relate it to entropy-variety divergences, aiming to bridge probabilistic and logical approaches for insights into causality and learning.
Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by several experiments with human subjects, yet its theoretical basis remains largely unexplored: why does it work? This paper lays the groundwork for three theoretical conjectures. First, unexpectedness can be seen as a generalization of Bayes' rule. Second, the frequentist core of unexpectedness can be connected to the function of tracking ergodic properties of the world. Third, unexpectedness can be seen as constituent of various measures of divergence between the entropy of the world (environment) and the variety of the observer (system). The resulting framework hints to research directions that go beyond the division between probabilistic and logical approaches, potentially bringing new insights into the extraction of causal relations, and into the role of descriptive mechanisms in learning.