Tao Yuan

Kang Zhao, Tao Yuan, Han Bao et al.

To date, 2:4 sparsity has stood as the only sparse pattern that can be accelerated using sparse tensor cores on GPUs. In practice, 2:4 sparsity often possesses low actual speedups ($\leq 1.3$) and requires fixed sparse ratios, meaning that other ratios, such as 4:8, 8:16, or those exceeding 50% sparsity, do not incur any speedups on GPUs. Recent studies suggest that V:N:M sparsity is promising in addressing these limitations of 2:4 sparsity. However, regarding accuracy, the effects of V:N:M sparsity on broader Transformer models, such as vision Transformers and large language models (LLMs), are largely unexamined. Moreover, Some specific issues related to V:N:M sparsity, such as how to select appropriate V and M values, remain unresolved. In this study, we thoroughly investigate the application of V:N:M sparsity in vision models and LLMs across multiple tasks, from pertaining to downstream tasks. We propose three key approaches to enhance the applicability and accuracy of V:N:M-sparse Transformers, including heuristic V and M selection, V:N:M-specific channel permutation, and three-staged LoRA training techniques. Experimental results show that, with our methods, the DeiT-small achieves lossless accuracy at 64:2:5 sparsity, while the DeiT-base maintains accuracy even at 64:2:8 sparsity. In addition, the fine-tuned LLama2-7B at 64:2:5 sparsity performs comparably or better than training-free 2:4 sparse alternatives on downstream tasks. More importantly, V:N:M-sparse Transformers offer a wider range of speedup-accuracy trade-offs compared to 2:4 sparsity. Overall, our exploration largely facilitates the V:N:M sparsity to act as a truly effective acceleration solution for Transformers in cost-sensitive inference scenarios.

Ziwei Li, Shuzi Niu, Tao Yuan et al.

Fill-ins are new nonzero elements in the summation of the upper and lower triangular factors generated during LU factorization. For large sparse matrices, they will increase the memory usage and computational time, and be reduced through proper row or column arrangement, namely matrix reordering. Finding a row or column permutation with the minimal fill-ins is NP-hard, and surrogate objectives are designed to derive fill-in reduction permutations or learn a reordering function. However, there is no theoretical guarantee between the golden criterion and these surrogate objectives. Here we propose to learn a reordering network by minimizing \(l_1\) norm of triangular factors of the reordered matrix to approximate the exact number of fill-ins. The reordering network utilizes a graph encoder to predict row or column node scores. For inference, it is easy and fast to derive the permutation from sorting algorithms for matrices. For gradient based optimization, there is a large gap between the predicted node scores and resultant triangular factors in the optimization objective. To bridge the gap, we first design two reparameterization techniques to obtain the permutation matrix from node scores. The matrix is reordered by multiplying the permutation matrix. Then we introduce the factorization process into the objective function to arrive at target triangular factors. The overall objective function is optimized with the alternating direction method of multipliers and proximal gradient descent. Experimental results on benchmark sparse matrix collection SuiteSparse show the fill-in number and LU factorization time reduction of our proposed method is 20% and 17.8% compared with state-of-the-art baselines.