Deep neural networks (DNNs) are traditionally analyzed as black-box function approximators, yet their internal structure exhibits phase transitions characteristic of complex physical systems. In this study, we investigate topological–functional decoupling—the phenomenon whereby a network retains full graph connectivity while losing computational function—in trained neural networks through the lens of percolation theory. By subjecting three distinct architectures (Shallow, Deep, and Wide MLPs) to a unified edge-pruning analysis on Fashion-MNIST, we uncover a fundamental divergence between structural integrity and computational capacity in this experimental setting. We report three key phenomena observed in these experiments: (1) the zombie network state under stochastic pruning, where the system retains global connectivity (P∞≈1.0) yet suffers a catastrophic functional collapse (accuracy falls below 50% of baseline at prunning ratio pf≈0.35–0.68 depending on depth), proves that graph reachability does not imply computational capability; (2) depth fragility, where increased network depth triggers multiplicative signal decay (the avalanche effect), rendering deep architectures exponentially more vulnerable to random edge removal than shallow ones (pfdeep≈0.35 vs. pfshallow≈0.68); and (3) scale-free universality, observed under magnitude-based pruning, where a robust functional skeleton maintains accuracy near the baseline (∼89%) up to extreme sparsity (pf≈0.85–0.95) across all three architectures. Robustness stems not from holographic redundancy in the overall connection count but from the emergent heavy-tailed rich-club organization of weight magnitudes—a sparse set of high-magnitude synapses that form the functional backbone of the network, decoupled from the redundant topological mass. These findings offer new physical constraints for the design of resilient neuromorphic hardware.
Nguyen et al. (Fri,) studied this question.