Bayes and Darwin: How replicator populations implement Bayesian computations.

Area of Science:

• Computational neuroscience
• Evolutionary biology
• Machine learning

Background:

• Bayesian learning and evolutionary theory model adaptive competition in complex environments.
• Both theories address adaptation in high-dimensional, varying, and noisy conditions.

Purpose of the Study:

• To explore commonalities and differences between Bayesian learning and evolutionary theory.
• To identify structural and dynamical analogies at computational and algorithmic levels.

Main Methods:

• Mathematical analysis of dynamical equations.
• Generalizing the isomorphism between Bayesian update and replicator dynamics.
• Comparing sampling approximations, particle filters, and the Wright-Fisher model.

Main Results:

• Demonstrated mathematical equivalences between basic dynamical equations of both theories.
• Showcased analogous mechanisms for adapting to stochastic environments across multiple timescales.
• Established algorithmic equivalence between particle filters and the Wright-Fisher model.

Conclusions:

• Frequency distributions in replicator populations optimally encode environmental regularities for prediction.
• A unified perspective on learning and evolution is achievable through these equivalences.
• These findings offer a new framework for understanding adaptation without invoking multilevel selection or evolvability.