# Are Straight-Through gradients and Soft-Thresholding all you need for Sparse Training?

arXiv: https://arxiv.org/abs/2212.01076 · HTML: https://mlsanity.com/paper/2212.01076/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 48 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [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)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Movement Pruning: Adaptive Sparsity by Fine-Tuning](https://mlsanity.com/paper/2005.07683/) (2020)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Accelerating Sparse Deep Neural Networks](https://mlsanity.com/paper/2104.08378/) (2021)
- [Efficient Neural Audio Synthesis](https://mlsanity.com/paper/1802.08435/) (2018)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [Ternary Weight Networks](https://mlsanity.com/paper/1605.04711/) (2016)
- [Pruning Neural Networks at Initialization: Why are We Missing the Mark?](https://mlsanity.com/paper/2009.08576/) (2020)
- [Soft Threshold Weight Reparameterization for Learnable Sparsity](https://mlsanity.com/paper/2002.03231/) (2020)
- [The Early Phase of Neural Network Training](https://mlsanity.com/paper/2002.10365/) (2020)
- [Do We Actually Need Dense Over-Parameterization? In-Time Over-Parameterization in Sparse Training](https://mlsanity.com/paper/2102.02887/) (2021)
- [Neural Pruning via Growing Regularization](https://mlsanity.com/paper/2012.09243/) (2020)

## Built on by (most cited first, 9 of 9)

- [Accurate Neural Network Pruning Requires Rethinking Sparse Optimization](https://mlsanity.com/paper/2308.02060/) (2023)
- [BLaST: High Performance Inference and Pretraining using BLock Sparse Transformers](https://mlsanity.com/paper/2507.03117/) (2025)
- [Effective Neural Network L0 Regularization With BinMask](https://mlsanity.com/paper/2304.11237/) (2023)
- [Edge Detectors Can Make Deep Convolutional Neural Networks More Robust](https://mlsanity.com/paper/2402.16479/) (2024)
- [AdapMTL: Adaptive Pruning Framework for Multitask Learning Model](https://mlsanity.com/paper/2408.03913/) (2024)
- [Feather: An Elegant Solution to Effective DNN Sparsification](https://mlsanity.com/paper/2310.02448/) (2023)
- [CAST: Continuous and Differentiable Semi-Structured Sparsity-Aware Training for Large Language Models](https://mlsanity.com/paper/2509.25996/) (2025)
- [SequentialAttention++ for Block Sparsification: Differentiable Pruning Meets Combinatorial Optimization](https://mlsanity.com/paper/2402.17902/) (2024)
- [Pruning Cannot Hurt Robustness: Certified Trade-offs in Reinforcement Learning](https://mlsanity.com/paper/2510.12939/) (2025)

## Abstract (arXiv)

Turning the weights to zero when training a neural network helps in reducing the computational complexity at inference. To progressively increase the sparsity ratio in the network without causing sharp weight discontinuities during training, our work combines soft-thresholding and straight-through gradient estimation to update the raw, i.e. non-thresholded, version of zeroed weights. Our method, named ST-3 for straight-through/soft-thresholding/sparse-training, obtains SoA results, both in terms of accuracy/sparsity and accuracy/FLOPS trade-offs, when progressively increasing the sparsity ratio in a single training cycle. In particular, despite its simplicity, ST-3 favorably compares to the most recent methods, adopting differentiable formulations or bio-inspired neuroregeneration principles. This suggests that the key ingredients for effective sparsification primarily lie in the ability to give the weights the freedom to evolve smoothly across the zero state while progressively increasing the sparsity ratio. Source code and weights available at https://github.com/vanderschuea/stthree