# Progressive Gradient Flow for Robust N:M Sparsity Training in Transformers

arXiv: https://arxiv.org/abs/2402.04744 · HTML: https://mlsanity.com/paper/2402.04744/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 76 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 30 of 58)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (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)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [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)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [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)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)

## Built on by (most cited first, 18 of 18)

- [A Survey: Collaborative Hardware and Software Design in the Era of Large Language Models](https://mlsanity.com/paper/2410.07265/) (2024)
- [SLoPe: Double-Pruned Sparse Plus Lazy Low-Rank Adapter Pretraining of LLMs](https://mlsanity.com/paper/2405.16325/) (2024)
- [Effective Interplay between Sparsity and Quantization: From Theory to Practice](https://mlsanity.com/paper/2405.20935/) (2024)
- [Sparse maximal update parameterization: A holistic approach to sparse training dynamics](https://mlsanity.com/paper/2405.15743/) (2024)
- [Demystifying AI Platform Design for Distributed Inference of Next-Generation LLM models](https://mlsanity.com/paper/2406.01698/) (2024)
- [SLiM: One-shot Quantization and Sparsity with Low-rank Approximation for LLM Weight Compression](https://mlsanity.com/paper/2410.09615/) (2024)
- [Re-Imagining Multimodal Instruction Tuning: A Representation View](https://mlsanity.com/paper/2503.00723/) (2025)
- [SparseLoRA: Accelerating LLM Fine-Tuning with Contextual Sparsity](https://mlsanity.com/paper/2506.16500/) (2025)
- [Enabling Unstructured Sparse Acceleration on Structured Sparse Accelerators](https://mlsanity.com/paper/2403.07953/) (2024)
- [S-STE: Continuous Pruning Function for Efficient 2:4 Sparse Pre-training](https://mlsanity.com/paper/2409.09099/) (2024)
- [Cut Less, Fold More: Model Compression through the Lens of Projection Geometry](https://mlsanity.com/paper/2602.18116/) (2026)
- [Navigating Extremes: Dynamic Sparsity in Large Output Spaces](https://mlsanity.com/paper/2411.03171/) (2024)
- [Beyond 2:4: exploring V:N:M sparsity for efficient transformer inference on GPUs](https://mlsanity.com/paper/2410.16135/) (2024)
- [The Journey Matters: Average Parameter Count over Pre-training Unifies Sparse and Dense Scaling Laws](https://mlsanity.com/paper/2501.12486/) (2025)
- [TAGC: Optimizing Gradient Communication in Distributed Transformer Training](https://mlsanity.com/paper/2504.05638/) (2025)
- [TSENOR: Highly-Efficient Algorithm for Finding Transposable N:M Sparse Masks](https://mlsanity.com/paper/2505.23949/) (2025)
- [DeVIT: Low-Power Vision Transformer Acceleration Using Delta Computation](https://mlsanity.com/paper/2608.01343/) (2026)
- [Compression Trinity: Exploring Sparsity, Quantization, and Low-Rank Approximations for LLM Compression](https://mlsanity.com/paper/2608.24070/) (2026)

## Abstract (arXiv)

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (~50%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80%). In this work, we study the effectiveness of existing sparse training recipes at textithigh-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressivegradientflownmsparsity.