When Sparsity Breaks Connectivity: Functional Reachability and Guided Topology Dynamics in Extreme Sparse Training

Dynamic Sparse Training (DST) methods train neural networks by maintaining sparsity while dynamically adapting the network topology. Despite the promise of reduced computation, DST methods converge significantly slower than dense training, often requiring comparable training time to achieve similar accuracy. We demonstrate both analytically and empirically that Batch Normalization (BN) adversely affects sparse training, and propose SparseOpt, a sparsity-aware optimizer, to address this. Experiments on ResNet models across CIFAR-100 and ImageNet demonstrate consistently faster convergence and improved generalization with our proposed method. Our work highlights the limitations of current normalization layers in sparse training and provides the first systematic study of the interaction between Batch Normalization, sparse layers, and DST, taking a significant step toward making DST practically competitive with dense training.

Profiled Sparse Networks (PSN) replace uniform connectivity with deterministic, heterogeneous fan-in profiles defined by continuous, nonlinear functions, creating neurons with both dense and sparse receptive fields. We benchmark PSN across four classification datasets spanning vision and tabular domains, input dimensions from 54 to 784, and network depths of 2--3 hidden layers. At 90% sparsity, all static profiles, including the uniform random baseline, achieve accuracy within 0.2-0.6% of dense baselines on every dataset, demonstrating that heterogeneous connectivity provides no accuracy advantage when hub placement is arbitrary rather than task-aligned. This result holds across sparsity levels (80-99.9%), profile shapes (eight parametric families, lognormal, and power-law), and fan-in coefficients of variation from 0 to 2.5. Internal gradient analysis reveals that structured profiles create a 2-5x gradient concentration at hub neurons compared to the ~1x uniform distribution in random baselines, with the hierarchy strength predicted by fan-in coefficient of variation ($r = 0.93$). When PSN fan-in distributions are used to initialise RigL dynamic sparse training, lognormal profiles matched to the equilibrium fan-in distribution consistently outperform standard ERK initialisation, with advantages growing on harder tasks, achieving +0.16% on Fashion-MNIST ($p = 0.036$, $d = 1.07$), +0.43% on EMNIST, and +0.49% on Forest Cover. RigL converges to a characteristic fan-in distribution regardless of initialisation. Starting at this equilibrium allows the optimiser to refine weights rather than rearrange topology. Which neurons become hubs matters more than the degree of connectivity variance, i.e., random hub placement provides no advantage, while optimisation-driven placement does.

Modern neural networks are heavily over-parameterized. This redundancy incurs substantial compute and memory overhead during training and inference. Existing pruning methods rely on post-hoc magnitude thresholds or static initialization heuristics. Consequently, they often require manual per-layer sparsity targets or expensive retraining cycles. We propose Dynamic Activity-Dependent Pruning (DADP), a biologically inspired structural plasticity mechanism. During training, DADP measures connection importance via the accumulated product of pre-synaptic activations and post-synaptic error gradients. Using a single global threshold instead of fixed layer budgets, DADP dynamically allocates sparsity across network depth while naturally inducing neuron- and channel-level pruning. Across MLP, VGG-16, ResNet-18, BiLSTM-CRF, and MiniBERT architectures, DADP matches or outperforms Magnitude, SNIP and RigL, retaining 73.67% accuracy (dense baseline: 76.06%) at 99% sparsity on ResNet-18. Finally, matrix-based Shannon entropy and effective rank measurements confirm that DADP preserves latent feature diversity at extreme sparsities without representation collapse.