Spectral Pruning of Deep Neural Networks via Adjacency Edge Index

This research introduces a new spectral pruning approach using the Adjacency Edge Index (AEI), which is a centrality measure from the theory of spectral graphs and first-order matrix perturbation theory. The AEI score reflects the contribution of each neuron to the network’s dynamic synchronizability via the Fiedler vector. The AEI approach thus offers a mathematically motivated saliency score in the context of data-driven neuron co-activation graphs. The proposed approach has been tested on MNIST, Fashion MNIST, KMNIST, and a real-world social network dataset. The approach has been extended to convolutional filter pruning on the CIFAR-10 dataset using spatial global average pooling. The AEI approach has been compared to magnitude-based pruning methods like L1 and L2 norms and gradient-based pruning methods like SNIP and GraSP. The robustness of the proposed approach has been established by comparing the results over five random seeds. The AEI approach is proposed as a principled, interpretable, structure-aware pruning criterion rather than an accuracy-maximising method. Spectral analysis demonstrates that AEI is the only evaluated method that systematically targets structurally peripheral neurons, whereas magnitude-based methods prune broadly across the structural spectrum and GraSP actively removes structurally central neurons, an effect most pronounced on more complex datasets and deeper architectures (CIFAR-100, ResNet-20), where it causes substantial accuracy degradation at high sparsity. The AEI approach has been extended to the Hybrid approach by combining the AEI and L2 norms. The Hybrid approach has been seen to improve the accuracy gap at 40% sparsity from 5.46 to 2.26 percentage points over the state of the art. The robustness of the proposed approach has been established by conducting ablation studies on the robustness of the approach to the selection of the graph. The approach has been seen to be moderately robust to the selection of the graph with Spearman’s ρ ≈ 0.70. The accuracy gap has been seen to be less than 0.2%.