Abstract: By forcing N out of M consecutive weights to be non-zero, the recent N:M fine-grained network sparsity has received increasing attention with its two attractive advantages over traditional irregular network sparsity methods: 1) Promising performance at a high sparsity. 2) Significant speedups when performed on NVIDIA A100 GPUs. Current implementation on N:M sparsity requires a tedious pre-training phase or computationally heavy from-scratch training. To circumvent these problems, this paper presents an efficient solution for achieving N:M fine-grained sparsity from scratch. Specifically, we first make a re-formulation to convert the N:M fine-grained sparsity into a combinatorial problem, in which, the object falls into choosing the best weight combination among $C_M^N$ candidates. Then, we equip each combination with a learnable importance score, which can be jointly optimized along with its associated weights. Through rigorous proof, we demonstrate that the magnitude of the optimized score well reflects the importance of its corresponding weights combination to the training loss. Therefore, by gradually removing combinations with smaller scores till the best one is left, N:M fine-grained sparsity can be efficiently optimized during the normal training phase without any extra expenditure. Comprehensive experimental results have demonstrated that our proposed method for learning best combination, dubbed as LBC, consistently increases the efficacy of the off-the-shelf N:M methods across varying networks and datasets. Our project is released at https://github.com/zyxxmu/LBC.