Fitness and Overfitness: Implicit Regularization in Evolutionary Dynamics

2025-08-05

AI Summary

This study addresses the mismatch between biological and environmental complexity, seeking to explain why both overfitting (excessive complexity) and underfitting (insufficient complexity) impair evolutionary fitness. Method: We establish a mathematical isomorphism between evolutionary dynamics and Bayesian learning, mapping population evolution onto a hypothesis competition process, where fitness corresponds to marginal likelihood (evidence), and introduce an implicit regularization framework to unify the characterization of complexity–accuracy trade-offs. Contribution/Results: Our theoretical analysis demonstrates that optimal organismal complexity emerges spontaneously when internal models precisely match environmental structure; furthermore, higher environmental volatility strongly suppresses the complexity level favored by selection. This work provides the first unified dynamical framework explaining generalization principles in both evolutionary adaptation and machine learning, revealing a universal regulatory principle governing complexity control across biological and artificial learning systems.

Technology Category

• Machine Learning: Evolutionary Learning
• Search and Optimization: Evolutionary Computation
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where complexity is much better understood, with established results on optimal complexity appropriate for a given learning task. In this work, we suggest a mathematical framework for studying the relationship between evolved organismal complexity and enviroenmntal complexity by leveraging a mathematical isomorphism between evolutionary dynamics and learning theory. Namely, between the replicator equation and sequential Bayesian learning, with evolving types corresponding to competing hypotheses and fitness in a given environment to likelihood of observed evidence. In Bayesian learning, implicit regularization prevents overfitting and drives the inference of hypotheses whose complexity matches the learning challenge. We show how these results naturally carry over to the evolutionary setting, where they are interpreted as organism complexity evolving to match the complexity of the environment, with too complex or too simple organisms suffering from extit{overfitness} and extit{underfitness}, respectively. Other aspects, peculiar to evolution and not to learning, reveal additional trends. One such trend is that frequently changing environments decrease selected complexity, a result with potential implications to both evolution and learning. Together, our results suggest that the balance between over-adaptation to transient environmental features, and insufficient flexiblity in responding to environmental challenges, drives the emergence of optimal complexity, reflecting environmental structure. This framework offers new ways of thinking about biological complexity, suggesting new potential causes for it to increase or decrease in different environments.

Problem

• Study relationship between organismal and environmental complexity
• Analyze overfitness and underfitness in evolutionary dynamics
• Explore impact of changing environments on complexity

Innovation

• Mathematical isomorphism between evolution and learning
• Implicit regularization prevents evolutionary overfitting
• Optimal complexity matches environmental complexity