# TSENOR: Highly-Efficient Algorithm for Finding Transposable N:M Sparse Masks

arXiv: https://arxiv.org/abs/2505.23949 · HTML: https://mlsanity.com/paper/2505.23949/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 68 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 30 of 43)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
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- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [End-to-end Autonomous Driving: Challenges and Frontiers](https://mlsanity.com/paper/2306.16927/) (2023)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Sustainable AI: Environmental Implications, Challenges and Opportunities](https://mlsanity.com/paper/2111.00364/) (2021)
- [Accelerating Sparse Deep Neural Networks](https://mlsanity.com/paper/2104.08378/) (2021)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [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)
- [Manifold Regularized Dynamic Network Pruning](https://mlsanity.com/paper/2103.05861/) (2021)
- [Fast as CHITA: Neural Network Pruning with Combinatorial Optimization](https://mlsanity.com/paper/2302.14623/) (2023)
- [Careful Selection of Knowledge to solve Open Book Question Answering](https://mlsanity.com/paper/1907.10738/) (2019)
- [STEP: Learning N:M Structured Sparsity Masks from Scratch with Precondition](https://mlsanity.com/paper/2302.01172/) (2023)
- [Accelerating Transformer Pre-training with 2:4 Sparsity](https://mlsanity.com/paper/2404.01847/) (2024)

## Abstract (arXiv)

Network pruning reduces the computational requirements of large neural networks, with N:M sparsity -- retaining only N out of every M consecutive weights -- offering a compelling balance between compressed model quality and hardware acceleration. However, N:M sparsity only accelerates forward-pass computations, as N:M patterns are not preserved during matrix transposition, limiting efficiency during training where both passes are computationally intensive. While transposable N:M sparsity has been proposed to address this limitation, existing methods for finding transposable N:M sparse masks either fail to scale to large models or are restricted to M=4 which results in suboptimal compression-accuracy trade-off. We introduce an efficient solver for transposable N:M masks that scales to billion-parameter models. We formulate mask generation as optimal transport problems and solve through entropy regularization and Dykstra's algorithm, followed by a rounding procedure. Our tensor-based implementation exploits GPU parallelism, achieving up to 100x speedup with only 1-10% error compared to existing methods. Our approach can be integrated with layer-wise N:M pruning frameworks including Wanda, SparseGPT and ALPS to produce transposable N:M sparse models with arbitrary N:M values. Experiments show that LLaMA3.2-8B with transposable 16:32 sparsity maintains performance close to its standard N:M counterpart and outperforms standard 2:4 sparse model, showing the practical value of our approach.