# A Unified Framework for Soft Threshold Pruning

arXiv: https://arxiv.org/abs/2302.13019 · HTML: https://mlsanity.com/paper/2302.13019/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 89 references that are in the map.
- First posted on arXiv 25 Feb 2023.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [Deep Residual Learning in Spiking Neural Networks](https://mlsanity.com/paper/2102.04159/) (2021)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [ParseNet: Looking Wider to See Better](https://mlsanity.com/paper/1506.04579/) (2015)
- [Drawing Early-Bird Tickets: Towards More Efficient Training of Deep Networks](https://mlsanity.com/paper/1909.11957/) (2019)
- [Soft Threshold Weight Reparameterization for Learnable Sparsity](https://mlsanity.com/paper/2002.03231/) (2020)
- [Do We Actually Need Dense Over-Parameterization? In-Time Over-Parameterization in Sparse Training](https://mlsanity.com/paper/2102.02887/) (2021)
- [Winning the Lottery with Continuous Sparsification](https://mlsanity.com/paper/1912.04427/) (2019)
- [Sparse Training via Boosting Pruning Plasticity with Neuroregeneration](https://mlsanity.com/paper/2106.10404/) (2021)
- [Top-KAST: Top-K Always Sparse Training](https://mlsanity.com/paper/2106.03517/) (2021)
- [Neural Architecture Search for Spiking Neural Networks](https://mlsanity.com/paper/2201.10355/) (2022)

## Built on by (most cited first, 12 of 12)

- [BESA: Pruning Large Language Models with Blockwise Parameter-Efficient Sparsity Allocation](https://mlsanity.com/paper/2402.16880/) (2024)
- [On the Opportunities of Green Computing: A Survey](https://mlsanity.com/paper/2311.00447/) (2023)
- [Magnitude Attention-based Dynamic Pruning](https://mlsanity.com/paper/2306.05056/) (2023)
- [Automatic Channel Pruning for Multi-Head Attention](https://mlsanity.com/paper/2405.20867/) (2024)
- [Model Compression Methods for YOLOv5: A Review](https://mlsanity.com/paper/2307.11904/) (2023)
- [GD doesn't make the cut: Three ways that non-differentiability affects neural network training](https://mlsanity.com/paper/2401.08426/) (2024)
- [SINF: Semantic Neural Network Inference with Semantic Subgraphs](https://mlsanity.com/paper/2310.01259/) (2023)
- [Dual sparse training framework: inducing activation map sparsity via Transformed ℓ1 regularization](https://mlsanity.com/paper/2405.19652/) (2024)
- [Toward Efficient Deep Spiking Neuron Networks:A Survey On Compression](https://mlsanity.com/paper/2407.08744/) (2024)
- [SPEAR: Structured Pruning for Spiking Neural Networks via Synaptic Operation Estimation and Reinforcement Learning](https://mlsanity.com/paper/2507.02945/) (2025)
- [SAFA-SNN: Sparsity-Aware On-Device Few-Shot Class-Incremental Learning with Fast-Adaptive Structure of Spiking Neural Network](https://mlsanity.com/paper/2510.03648/) (2025)
- [Performance and Complexity Trade-off Optimization of Speech Models During Training](https://mlsanity.com/paper/2601.13704/) (2026)

## Abstract (arXiv)

Soft threshold pruning is among the cutting-edge pruning methods with state-of-the-art performance. However, previous methods either perform aimless searching on the threshold scheduler or simply set the threshold trainable, lacking theoretical explanation from a unified perspective. In this work, we reformulate soft threshold pruning as an implicit optimization problem solved using the Iterative Shrinkage-Thresholding Algorithm (ISTA), a classic method from the fields of sparse recovery and compressed sensing. Under this theoretical framework, all threshold tuning strategies proposed in previous studies of soft threshold pruning are concluded as different styles of tuning L1-regularization term. We further derive an optimal threshold scheduler through an in-depth study of threshold scheduling based on our framework. This scheduler keeps L1-regularization coefficient stable, implying a time-invariant objective function from the perspective of optimization. In principle, the derived pruning algorithm could sparsify any mathematical model trained via SGD. We conduct extensive experiments and verify its state-of-the-art performance on both Artificial Neural Networks (ResNet-50 and MobileNet-V1) and Spiking Neural Networks (SEW ResNet-18) on ImageNet datasets. On the basis of this framework, we derive a family of pruning methods, including sparsify-during-training, early pruning, and pruning at initialization. The code is available at https://github.com/Yanqi-Chen/LATS.