Functional Degeneracy in Neural Networks: Measurement and Pruning

Neural network compression is commonly achieved by pruning parameters based on local importance scores, e.g., magnitude-based pruning. We propose a complementary approach that compresses models by aggregating neurons with similar functional behavior rather than removing weights independently. Our method encodes a trained network as a polynomial ODE system and applies a lumping method called Approximate Forward Differential Equivalence to identify neurons with approximately matching induced dynamics. A single tolerance parameter, $\varepsilon$, controls the compression level and induces a smooth trade-off between model size and predictive accuracy. We evaluate the method on synthetic datasets derived from nonlinear dynamical systems with known ground-truth behavior and on public regression benchmarks. Across both settings, the proposed approach achieves substantial parameter reduction while preserving accuracy, and consistently compares favorably with magnitude-based pruning and Wanda at similar compression levels. These results suggest that differential equivalence-based aggregation is a principled and effective alternative to conventional weight-centric pruning.

We identify a Selection Plateau phenomenon in one-shot neural network pruning: all rank-monotone weight scorers converge to identical accuracy at fixed sparsity, independent of functional form. We propose the Sparsity-Information-Complexity Spectrum (SICS) hypothesis: a sparsity-dependent minimum feature complexity kappa(S) governs plateau escape, with kappa=0 sufficient at low sparsity (S<0.65), kappa=1 dominant at critical sparsity (S~0.7), and kappa=2 necessary at extreme sparsity (S>0.75). On ViT-Small/CIFAR-10, testing nine feature classes across four sparsities, smooth non-monotone features provide +6.6% escape at S=0.7, while only raw features with high-frequency wiggle escape at S=0.8 (+2.6%). A fake non-monotone scorer underperforms the gradient baseline, indicating the requirement is magnitude-independent non-monotonicity. A handcrafted Gaussian bump achieves only +0.006 escape vs. chaos-derived +0.046, indicating rank-alignment is necessary but insufficient. SICS provides a unifying explanation for the performance clustering of diverse pruning methods and suggests that future selection algorithms should adapt feature complexity to target sparsity.

Structured pruning is a model compression technique that is used to reduce the computational cost of deploying deep neural networks on resource-constrained devices. Popular methods of pruning rely on opaque heuristics or weight-based criteria that give no indication as to the structural dependencies in the network. To address these limitations we present Artificial Structure Function Search (ASF-S): a novel structured pruning framework. ASF-S utilizes Principle Gradient Importance (PGI): a novel prune-candidate selection criteria that is inspired by structure-function relationships in the brain. By ensuring the pruned structure of the model respects topographical organization of the output layer, we define Artificial Functional Connectivity (AFC) for artificial neural networks. AFC provides evidence to demonstrate that accurate smaller networks can be found using careful prune candidate selection criteria. We present results for PGI as a selection criterion and for ASF-S as a pruning framework against recent benchmarks, demonstrating that our method yields model variants with 70% parameter reduction, that can recover baseline accuracy without re-training the pruned layers.