Dynamic Sparse Training

Dynamic Sparse Training (DST) periodically prunes and regrows connections, inducing a discrete dynamical mechanism over network topologies. At extreme sparsity ($\ge 99\%$), this dynamic tends to destroy input-output information pathways, and performance with standard magnitude/random updates degrades sharply. We formalize forward, backward, and functional reachability on layered sparse graphs, derive closed-form expectations for reachable neurons and edges, and show that Monte Carlo realizations match the theory. Guided by this reachability-based structure, we bias pruning toward non-functional edges and regrowth toward functionally consistent candidates. We introduce this reachability-driven modification of topology evolution as Reachability-guided in DST, referred to as guided DST. On CIFAR-10/100 and Tiny ImageNet, guided DST recovers large accuracy gaps versus unguided DST (up to $+14.4$ points at $99.9\%$ sparsity on CIFAR-100), and on MLP-Mixer guided DST remains trainable at $99.99\%$ sparsity while unguided random regrowth degrades sharply. These results cast extreme-sparse training as a connectivity-preserving dynamical process. Our implementation is publicly available at https://github.com/mzjaworski/ea_dst.

Dynamic sparse training (DST) aims to reduce training costs while maintaining accuracy. Existing DST methods mask out parameters but keep matrix dimensions unchanged. Training speedups therefore depend on specialized support, such as sparse kernels. We introduce BARTER, a structured DST framework that reduces training cost using standard dense kernels by keeping training tensors physically compact while dynamically reallocating capacity across layers. Unlike existing works that require computing gradients for all parameters, BARTER instead uses statistics collected only from active units during ordinary backpropagation to prune and clone attention heads and feed-forward channels under separate fixed global budgets. At each topology update, it resizes the affected parameter tensors and remaps their optimizer states, so subsequent training steps operate directly on the compact model. Training and fine-tuning experiments with Transformer-based vision models on two image classification benchmarks at densities from $0.1$ to $0.7$ show competitive Top-1 accuracy relative to full-tensor DST baselines. On an NVIDIA L40, BARTER achieves speedups of up to $6.29\times$ in measured training segments and reduces peak allocated GPU memory by up to $81.3\%$ relative to these implementations. An iPhone 13 Pro Max training benchmark additionally shows a $2.78\times$ speedup over the full-tensor DST baseline.

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.

Deep neural networks continue to grow in parameter count, driving up training and inference cost on GPUs. Sparse neural networks and Dynamic Sparse Training (DST) promise to reduce these costs, but most implementations rely on binary masks over dense tensors and recover little of the theoretical compute, memory, or energy savings. We propose SNACK, a truly sparse GPU layer that stores and computes only non-zero connections. SNACK exposes a simple PyTorch API for restructuring connections and backpropagating gradients entirely in the sparse paradigm, and ships SNACK-COO, a custom COO-format SpMM CUDA kernel with a batch-to-Streaming-Multiprocessor mapping tuned for the small-batch, high-sparsity regime typical of large-model training and single-stream inference. At the kernel level, SNACK is up to 7x faster than the masked dense baseline (Dense+Mask) and competitive with cuSPARSE, Sputnik, and FlashSparse at 95% sparsity. At 90% sparsity, a single SNACK layer accelerates training by 8x and 3.7x, and inference by 4x and 2x, over Dense+Mask and fully dense layers, respectively, while using 72% less memory than dense and substantially less energy. End-to-end, SNACK reduces GPT-2 peak training memory by up to 40% and graph-style inference latency by 4.8x over Dense+Mask at 99% sparsity.

Extreme multi-label classification (XMC) involves learning models over large output spaces with millions of labels, making the output layer a memory-compute bottleneck. While sparsity-based methods reduce arithmetic complexity, they often fail to yield proportional speedups due to irregular memory access, poor hardware utilization, or reliance on auxiliary architectural components in long-tailed regimes. We introduce group-shared fixed fan-in sparsity, a semi-structured output-layer design in which semantically related labels share a sparse input pattern while retaining independent weights. This grouping introduces a task-aligned inductive bias -- encouraging related labels to share feature subsets -- while reducing index memory overhead, increasing feature reuse across labels, and enabling efficient GPU execution via custom CUDA kernels that leverage modern accelerator primitives. As an alternative to auxiliary objectives, we exploit the long-tailed structure of XMC by decomposing the output layer into a small dense head over frequent labels and a group-shared sparse tail over the remainder, providing an informative gradient pathway while preserving the memory benefits of sparsity. Through kernel-level microbenchmarking, we show that group-shared fixed fan-in translates arithmetic reductions into practical wall-clock gains, achieving up to $4.4\times$ speedup in the forward pass and up to $25\times$ speedup in backward passes over standard fixed fan-in sparsity, while operating within a few percent of a FLOPs-matched dense bottleneck. Across large-scale XMC benchmarks, our approach matches or improves precision@k over prior sparse baselines, while narrowing the performance gap to dense.

Dynamic Sparse Training (DST) offers a promising paradigm for improving the training and inference efficiency of deep neural networks; however, we find that in large language model training, DST can suffer from optimization instability, manifested as loss spikes after topology updates. In this work, we show that the naive use of standard Adam-based optimizers leads to a cold-start issue for newly regrown parameters, resulting in excessively large updates and disrupted training dynamics. To address this issue, we propose Sparse Memory-Efficient Training (SMET), which stabilizes DST with optimizer warm-up and improves training progress through density-aware learning-rate scaling. SMET further reduces memory consumption by storing gradients and optimizer states only for active parameters. We provide a theoretical analysis of the update behaviors under SMET, showing improved optimization stability. Extensive experiments demonstrate that SMET enables stable, scalable, and memory-efficient sparse pre-training of LLMs, paving the way for sparse training as a practical alternative to dense training. Our code is publicly available at: https://github.com/QiaoXiao7282/SMET.

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.

This paper introduces Growing Networks with Autonomous Pruning (GNAP) for image classification. Unlike traditional convolutional neural networks, GNAP change their size, as well as the number of parameters they are using, during training, in order to best fit the data while trying to use as few parameters as possible. This is achieved through two complementary mechanisms: growth and pruning. GNAP start with few parameters, but their size is expanded periodically during training to add more expressive power each time the network has converged to a saturation point. Between these growing phases, model parameters are trained for classification and pruned simultaneously, with complete autonomy by gradient descent. Growing phases allow GNAP to improve their classification performance, while autonomous pruning allows them to keep as few parameters as possible. Experimental results on several image classification benchmarks show that our approach can train extremely sparse neural networks with high accuracy. For example, on MNIST, we achieved 99.44% accuracy with as few as 6.2k parameters, while on CIFAR10, we achieved 92.2\ accuracy with 157.8k parameters.

We investigate the robustness of sparse artificial neural networks trained with adaptive topology. We focus on a simple yet effective architecture consisting of three sparse layers with 99% sparsity followed by a dense layer, applied to image classification tasks such as MNIST and Fashion MNIST. By updating the topology of the sparse layers between each epoch, we achieve competitive accuracy despite the significantly reduced number of weights. Our primary contribution is a detailed analysis of the robustness of these networks, exploring their performance under various perturbations including random link removal, adversarial attack, and link weight shuffling. Through extensive experiments, we demonstrate that adaptive topology not only enhances efficiency but also maintains robustness. This work highlights the potential of adaptive sparse networks as a promising direction for developing efficient and reliable deep learning models.