# Bi-directional Masks for Efficient N:M Sparse Training

arXiv: https://arxiv.org/abs/2302.06058 · HTML: https://mlsanity.com/paper/2302.06058/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 13 Feb 2023.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [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)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [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)
- [Movement Pruning: Adaptive Sparsity by Fine-Tuning](https://mlsanity.com/paper/2005.07683/) (2020)
- [HRank: Filter Pruning using High-Rank Feature Map](https://mlsanity.com/paper/2002.10179/) (2020)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [MetaPruning: Meta Learning for Automatic Neural Network Channel Pruning](https://mlsanity.com/paper/1903.10258/) (2019)
- [Sparse Networks from Scratch: Faster Training without Losing Performance](https://mlsanity.com/paper/1907.04840/) (2019)
- [Parameter Efficient Training of Deep Convolutional Neural Networks by Dynamic Sparse Reparameterization](https://mlsanity.com/paper/1902.05967/) (2019)
- [Learning N:M Fine-grained Structured Sparse Neural Networks From Scratch](https://mlsanity.com/paper/2102.04010/) (2021)
- [Accelerated Sparse Neural Training: A Provable and Efficient Method to Find N:M Transposable Masks](https://mlsanity.com/paper/2102.08124/) (2021)
- [Pruning Filter in Filter](https://mlsanity.com/paper/2009.14410/) (2020)
- [Learning Best Combination for Efficient N:M Sparsity](https://mlsanity.com/paper/2206.06662/) (2022)
- [An Algorithm-Hardware Co-Optimized Framework for Accelerating N:M Sparse Transformers](https://mlsanity.com/paper/2208.06118/) (2022)
- [Minimum Variance Unbiased N:M Sparsity for the Neural Gradients](https://mlsanity.com/paper/2203.10991/) (2022)

## Built on by (most cited first, 13 of 13)

- [SLoPe: Double-Pruned Sparse Plus Lazy Low-Rank Adapter Pretraining of LLMs](https://mlsanity.com/paper/2405.16325/) (2024)
- [TeleSparse: Practical Privacy-Preserving Verification of Deep Neural Networks](https://mlsanity.com/paper/2504.19274/) (2025)
- [S-STE: Continuous Pruning Function for Efficient 2:4 Sparse Pre-training](https://mlsanity.com/paper/2409.09099/) (2024)
- [Systematic Investigation of Sparse Perturbed Sharpness-Aware Minimization Optimizer](https://mlsanity.com/paper/2306.17504/) (2023)
- [Beyond 2:4: exploring V:N:M sparsity for efficient transformer inference on GPUs](https://mlsanity.com/paper/2410.16135/) (2024)
- [Spatial Re-parameterization for N:M Sparsity](https://mlsanity.com/paper/2306.05612/) (2023)
- [MaxQ: Multi-Axis Query for N:M Sparsity Network](https://mlsanity.com/paper/2312.07061/) (2023)
- [TSENOR: Highly-Efficient Algorithm for Finding Transposable N:M Sparse Masks](https://mlsanity.com/paper/2505.23949/) (2025)
- [Extreme Model Compression with Structured Sparsity at Low Precision](https://mlsanity.com/paper/2511.08360/) (2025)
- [RNM-TD3: N:M Semi-structured Sparse Reinforcement Learning From Scratch](https://mlsanity.com/paper/2602.14578/) (2026)
- [Robustness in sparse artificial neural networks trained with adaptive topology](https://mlsanity.com/paper/2602.21961/) (2026)
- [ELAS: Efficient Pre-Training of Low-Rank Large Language Models via 2:4 Activation Sparsity](https://mlsanity.com/paper/2605.03667/) (2026)
- [Compression Trinity: Exploring Sparsity, Quantization, and Low-Rank Approximations for LLM Compression](https://mlsanity.com/paper/2608.24070/) (2026)

## Abstract (arXiv)

We focus on addressing the dense backward propagation issue for training efficiency of N:M fine-grained sparsity that preserves at most N out of M consecutive weights and achieves practical speedups supported by the N:M sparse tensor core. Therefore, we present a novel method of Bi-directional Masks (Bi-Mask) with its two central innovations in: 1) Separate sparse masks in the two directions of forward and backward propagation to obtain training acceleration. It disentangles the forward and backward weight sparsity and overcomes the very dense gradient computation. 2) An efficient weight row permutation method to maintain performance. It picks up the permutation candidate with the most eligible N:M weight blocks in the backward to minimize the gradient gap between traditional uni-directional masks and our bi-directional masks. Compared with existing uni-directional scenario that applies a transposable mask and enables backward acceleration, our Bi-Mask is experimentally demonstrated to be more superior in performance. Also, our Bi-Mask performs on par with or even better than methods that fail to achieve backward acceleration. Project of this paper is available at urlhttps://github.com/zyxxmu/Bi-Mask.