Pruning as Evolution: Emergent Sparsity Through Selection Dynamics in Neural Networks

Neural networks are commonly trained in highly overparameterized regimes, yet empirical evidence consistently shows that many parameters become redundant during learning. Most existing pruning approaches impose sparsity through explicit intervention, such as importance-based thresholding or regularization penalties, implicitly treating pruning as a centralized decision applied to a trained model. This assumption is misaligned with the decentralized, stochastic, and path-dependent character of gradient-based training. We propose an evolutionary perspective on pruning: parameter groups (neurons, filters, heads) are modeled as populations whose influence evolves continuously under selection pressure. Under this view, pruning corresponds to population extinction: components with persistently low fitness gradually lose influence and can be removed without discrete pruning schedules and without requiring equilibrium computation. We formalize neural pruning as an evolutionary process over population masses, derive selection dynamics governing mass evolution, and connect fitness to local learning signals. We validate the framework on MNIST using a population-scaled MLP (784--512--256--10) with 768 prunable neuron populations. All dynamics reach dense baselines near 98\% test accuracy. We benchmark post-training hard pruning at target sparsity levels (35--50\%): pruning 35\% yields $\approx$95.5\% test accuracy, while pruning 50\% yields $\approx$88.3--88.6\%, depending on the dynamic. These results demonstrate that evolutionary selection produces a measurable accuracy--sparsity tradeoff without explicit pruning schedules during training.

Pruning as a Game: Equilibrium-Driven Sparsification of Neural Networks

Neural network pruning is widely used to reduce model size and computational cost. Yet, most existing methods treat sparsity as an externally imposed constraint, enforced through heuristic importance scores or training-time regularization. In this work, we propose a fundamentally different perspective: pruning as an equilibrium outcome of strategic interaction among model components. We model parameter groups such as weights, neurons, or filters as players in a continuous non-cooperative game, where each player selects its level of participation in the network to balance contribution against redundancy and competition. Within this formulation, sparsity emerges naturally when continued participation becomes a dominated strategy at equilibrium. We analyze the resulting game and show that dominated players collapse to zero participation under mild conditions, providing a principled explanation for pruning behavior. Building on this insight, we derive a simple equilibrium-driven pruning algorithm that jointly updates network parameters and participation variables without relying on explicit importance scores. This work focuses on establishing a principled formulation and empirical validation of pruning as an equilibrium phenomenon, rather than exhaustive architectural or large-scale benchmarking. Experiments on standard benchmarks demonstrate that the proposed approach achieves competitive sparsity-accuracy trade-offs while offering an interpretable, theory-grounded alternative to existing pruning methods.