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We introduce channel permutations as a method to maximize the accuracy of N:M sparse networks. N:M sparsity requires N out of M consecutive elements to be zero and has been shown to maintain accuracy for many models and tasks with a simple prune and fine-tune workflow. By permuting weight matrices along their channel dimension and adjusting the surrounding layers appropriately, we demonstrate accuracy recovery for even small, parameter-efficient networks, without affecting inference run-time. We also present both a quality metric to simplify judging permutations as well as efficient methods to search for high-quality permutations, including two optimizations to escape local minima. Finally, we share an ablation study to show the importance of each part of our search algorithm, experimental results showing correlation between our quality metric and final network accuracy, improved sparse network accuracy using our techniques with insignificant overhead to training time, and the transformation of unstructured to structured sparse workloads.

Channel permutation is a powerful technique for enhancing the accuracy of N:M sparse models by reordering the channels of weight matrices to prioritize the retention of important weights. However, traditional channel permutation methods rely on handcrafted quality metrics, which often fail to accurately capture the true impact of pruning on model performance. To address this limitation, we propose PermLLM, a novel post-training pruning framework that introduces learnable channel permutation (LCP) for N:M sparsity. LCP leverages Sinkhorn normalization to transform discrete permutation matrices into differentiable soft permutation matrices, enabling end-to-end optimization. Additionally, PermLLM incorporates an efficient block-wise channel permutation strategy, which significantly reduces the number of learnable parameters and computational complexity. PermLLM seamlessly integrates with existing one-shot pruning methods to adaptively optimize channel permutations, effectively mitigating pruning-induced errors. Extensive experiments on the LLaMA series, Qwen, and OPT models demonstrate that PermLLM achieves superior performance in optimizing N:M sparse models. The code is available at https://github.com/lanchengzou/PermLLM.

We introduce channel permutations as a method to maximize the accuracy of N:M sparse networks. N:M sparsity requires N out of M consecutive elements to be zero and has been shown to maintain accuracy for many models and tasks with a simple prune and fine-tune workflow. By permuting weight matrices along their channel dimension and adjusting the surrounding layers appropriately, we demonstrate accuracy recovery for even small, parameter-efficient networks, without affecting inference run-time. We also present both a quality metric to simplify judging permutations as well as efficient methods to search for high-quality permutations, including two optimizations to escape local minima. Finally, we share an ablation study to show the importance of each part of our search algorithm, experimental results showing correlation between our quality metric and final network accuracy, improved sparse network accuracy using our techniques with insignificant overhead to training time, and the transformation of unstructured to structured sparse workloads.

N:M sparsity pruning is a powerful technique for compressing deep neural networks, utilizing NVIDIA's Sparse Tensor Core technology. This method benefits from hardware support for sparse indexing, enabling the adoption of fine-grained sparsity to maintain model accuracy while minimizing the overhead typically associated with irregular data access. Although restricted to a fixed level of sparsity due to its reliance on hardware, N:M sparsity can be combined with coarser sparsity techniques to achieve diverse compression ratios. Initially, column-wise vector sparsity is applied to a dense model, followed by row-wise N:M sparsity on the preserved column vectors. We call this multi-level approach as hierarchical N:M (HiNM) sparsity. Similar to earlier single-level sparsity techniques, HiNM sparsity necessitates an effective channel permutation strategy to maximize the accuracy of the compressed networks. However, it introduces further complexities by requiring the rearrangement of both input and output channels, addressing challenges such as permutation sequence, HiNM-sparsity-aware permutation, and maintaining consistency in channel ordering across layers. In this paper, we introduce a channel permutation method designed specifically for HiNM sparsity, named gyro-permutation. This method is crafted to exploit the unique characteristics of HiNM pruning, incorporating a strategic policy in each permutation phase, including channel sampling, clustering, and assignment, to circumvent local minima. Additionally, we have developed a GPU kernel that facilitates independent layer permutation during the execution of HiNM sparse networks. Our extensive experimental evaluations on various DNN models demonstrate that our gyro-permutation significantly enhances the accuracy of HiNM sparse networks, allowing them to reach performance levels comparable to those of unstructured sparse networks.

We introduce two methods for improving the performance of agents meeting for the first time to accomplish a communicative task. The methods are: (1) `message mutation' during the generation of the communication protocol; and (2) random permutations of the communication channel. These proposals are tested using a simple two-player game involving a `teacher' who generates a communication protocol and sends a message, and a `student' who interprets the message. After training multiple agents via self-play we analyse the performance of these agents when they are matched with a stranger, i.e. their zero-shot communication performance. We find that both message mutation and channel permutation positively influence performance, and we discuss their effects.