# S-STE: Continuous Pruning Function for Efficient 2:4 Sparse Pre-training

arXiv: https://arxiv.org/abs/2409.09099 · HTML: https://mlsanity.com/paper/2409.09099/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 52 references that are in the map.
- First posted on arXiv 13 Sep 2024.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [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)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [The Lottery Ticket Hypothesis for Pre-trained BERT Networks](https://mlsanity.com/paper/2007.12223/) (2020)
- [Accelerating Sparse Deep Neural Networks](https://mlsanity.com/paper/2104.08378/) (2021)
- [Learning N:M Fine-grained Structured Sparse Neural Networks From Scratch](https://mlsanity.com/paper/2102.04010/) (2021)
- [Block Pruning For Faster Transformers](https://mlsanity.com/paper/2109.04838/) (2021)
- [Training Deep Neural Networks with 8-bit Floating Point Numbers](https://mlsanity.com/paper/1812.08011/) (2018)
- [Drawing Early-Bird Tickets: Towards More Efficient Training of Deep Networks](https://mlsanity.com/paper/1909.11957/) (2019)
- [Convergence Analysis of Two-layer Neural Networks with ReLU Activation](https://mlsanity.com/paper/1705.09886/) (2017)
- [Accelerated Sparse Neural Training: A Provable and Efficient Method to Find N:M Transposable Masks](https://mlsanity.com/paper/2102.08124/) (2021)
- [EarlyBERT: Efficient BERT Training via Early-bird Lottery Tickets](https://mlsanity.com/paper/2101.00063/) (2020)

## Built on by (most cited first, 7 of 7)

- [BLaST: High Performance Inference and Pretraining using BLock Sparse Transformers](https://mlsanity.com/paper/2507.03117/) (2025)
- [HASTE: Hardware-Aware Dynamic Sparse Training for Large Output Spaces](https://mlsanity.com/paper/2606.01117/) (2026)
- [Vanishing Contributions: A Unified Framework for Smooth and Iterative Model Compression](https://mlsanity.com/paper/2510.09696/) (2025)
- [Extreme Model Compression with Structured Sparsity at Low Precision](https://mlsanity.com/paper/2511.08360/) (2025)
- [Learnable Permutation for Structured Sparsity on Transformer Models](https://mlsanity.com/paper/2601.22980/) (2026)
- [To 2:4 Sparsity and Beyond: Neuron-level Activation Function to Accelerate LLM Pre-Training](https://mlsanity.com/paper/2602.06183/) (2026)
- [ELAS: Efficient Pre-Training of Low-Rank Large Language Models via 2:4 Activation Sparsity](https://mlsanity.com/paper/2605.03667/) (2026)

## Abstract (arXiv)

Training deep neural networks (DNNs) is costly. Fortunately, Nvidia Ampere and Hopper GPUs can accelerate matrix multiplications twice as fast as a dense equivalent by implementing 2:4 sparsity. However, previous STE-based 2:4 pre-training methods (e.g. STE with hard-thresholding, SR-STE) suffer from optimization difficulties because of discontinuous pruning function. In this study, we comprehensively analyse the bottleneck of traditional N:M sparse training and recognize three drawbacks with discontinuity: incorrect descending direction, inability to predict the amount of descent and sparse mask oscillation. In light of this, we propose S-STE, a simple yet powerful 2:4 training method that contains two parts: to continuously project weights to be 2:4 sparse, and to rescale sparse weights with a per-tensor fixed scaling factor. Besides, we adopt minimum-variance unbiased estimation for activation gradient and FP8 quantization for whole process. Results show that our method surpasses previous 2:4 pre-training recipes and is comparable even with full parameter models. Our toolkit is available at https://github.com/huyz2023/2by4-pretrain.