This paper introduces SparseOptimizer, a novel deep learning optimizer that exploits Moreau-Yosida regularization to naturally induce sparsity in large language models such as BERT, ALBERT and GPT. Key to the design of SparseOptimizer is an embedded shrinkage operator, which imparts sparsity directly within the optimization process. This operator, backed by a sound theoretical framework, includes an analytical solution, thereby reinforcing the optimizer's robustness and efficacy. Crucially, SparseOptimizer's plug-and-play functionality eradicates the need for code modifications, making it a universally adaptable tool for a wide array of large language models. Empirical evaluations on benchmark datasets such as GLUE, RACE, SQuAD1, and SQuAD2 confirm that SparseBERT and SparseALBERT, when sparsified using SparseOptimizer, achieve performance comparable to their dense counterparts, BERT and ALBERT, while significantly reducing their parameter count. Further, this work proposes an innovative optimizer-compiler co-design strategy, demonstrating the potential of inference acceleration (\textbf{3.37x}, \textbf{6.30x}, and \textbf{7.15x} in comparison with Pytorch, TensorFlow, and LLVM generic compile, respectively) in SparseBERT when paired with an appropriately designed compiler. This study represents a significant step forward in the evolution of efficient, scalable, and high-performing large language models, setting a precedent for future exploration and optimization in this domain. The SparseOptimizer code and SparseALBERT model will be made available upon paper acceptance.

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