A Unified Framework for Quantized and Continuous Strong Lottery Tickets

The Strong Lottery Ticket Hypothesis (SLTH) asserts that sufficiently overparameterized, randomly initialized neural networks contain sparse subnetworks that, even without any training, can match the performance of a small trained network on a given dataset. A key mathematical tool in the theoretical study of SLTH has been the Random Subset Sum Problem (RSSP). The SLTH has recently been extended to the quantized setting, where the network weights are sampled from a discrete set rather than from a continuous interval. These new results are however far from those in arbitrary-precision setting in several ways. In this work, we provide an analysis of the RSSP in the discrete setting, and use it to derive tight SLTH guarantees in the quantized case. Our analysis obtain tight bounds on the failure probability of finding a strong lottery ticket in the quantized regime, providing an exponential improvement over previous results. Most importantly, it unifies the literature by showing that both approximate representations in the continuous setting and exact representations in quantized settings naturally emerge as limiting cases of our results. This perspective not only sharpens existing bounds but also provides a cohesive framework that simultaneously handles approximation and rounding errors.

Finding Sparse Subnetworks in One Training Cycle via Progressive Magnitude-Based Pruning

Neural network pruning reduces model size by removing less important parameters while aiming to preserve predictive performance. Although the Lottery Ticket Hypothesis (LTH) shows that sparse subnetworks can match dense networks when trained from suitable initializations, its iterative pruning procedure requires multiple complete training cycles. This work evaluates progressive magnitude-based pruning as a single-cycle alternative. The method gradually increases sparsity during training using a linear schedule and updates pruning masks based on active weight magnitudes. We conduct systematic experiments on CIFAR-10 and MNIST across ResNet, VGG-style, and LeNet architectures, comparing the proposed method with representative iterative and initialization-based pruning baselines, including LTH, SNIP, and GraSP. On CIFAR-10, the method achieves 95.12\% accuracy on ResNet-18 at 72.9\% sparsity, compared with 90.5\% reported for LTH. At extreme sparsity, it achieves 93.13\% accuracy on a VGG-like architecture at 97\% sparsity, compared with approximately 92.0\% for SNIP, and 93.44\% accuracy on VGG-19 at 97.97\% sparsity, compared with 92.19\% for GraSP at 98\% sparsity. A sparsity-accuracy analysis on ResNet-18 further shows that accuracy remains within 0.1 percentage points of the dense baseline across 70--85\% sparsity. These results indicate that progressive magnitude-based pruning provides an effective single-cycle approach for neural network sparsification under the evaluated settings.