Title: Neural Darwinism: A Theoretical Framework for Representation Evolution in Convolutional Neural Networks
Primary area: learning theory
Keywords: Neural Darwinism, Darwinian Score, Neural Darwinian Culling, Convolutional Neural Networks

Abstract: We propose a Darwinian framework that provides a mathematical foundation for neural representation dynamics, conceptualizing deep learning as an evolutionary process governed by selection and adaptation. In this framework, neurons are treated as competing entities whose survival is determined by a Darwinian Score, a derived fitness measure  reflecting the informational richness, functional relevance, and adaptive dynamics of neural activity over training. This score induces a constrained optimization problem that explicitly balances model compactness with predictive fidelity, from which we derive theoretical guarantees on approximation error. Building on this foundation, we introduce Neural Darwinian Culling (NDC), a practical algorithm that adaptively eliminates neurons of low evolutionary fitness during training while preserving high-value units. Experiments on standard vision benchmarks show that NDC achieves substantially higher sparsity with improved generalization compared to state-of-the-art pruning methods, and ablation studies confirm the effectiveness of the Darwinian Score as a unifying principle. Our work thus establishes both a general evolutionary framework of neural representation and its operational realization for efficient deep learning.