Triple equivalence in modelling insight and creativity: Classical and quantum perspectives

Understanding the emergence of novel ideas in the brain-which is a hallmark of insight and creativity-remains a fundamental challenge in neuroscience. While traditional frameworks such as predictive coding, the Bayesian brain hypothesis, and the free-energy principle emphasise the approximation of external milieu states, internal generative processes that create new ideas rather than imitate remain underexplored. This review proposes a normative account of insight and creativity grounded in a triple equivalence between neural dynamics, Bayesian inference, and algorithmic computation. This equivalence provides a formal framework for understanding how neural circuits driven by mental actions can spontaneously generate creative ideas. Moreover, such creativity requires an efficient exploration of the algorithmic space to minimise free energy. Insight corresponds to a non-local search strategy that enables escape from local minima, thereby distinguishing it from conventional predictive processing. To this end, quasi-quantum neural networks that leverage superpositional coding can be considered to account for efficient global search. From this perspective, insight and creativity emerge through a self-organising exploratory process, offering a view of the brain as a spontaneous algorithm generator, rather than a predictor of its external milieu.