SMMF: Square-Matricized Momentum Factorization for Memory-Efficient Optimization

• URL: http://arxiv.org/abs/2412.08894v2
• Date: Fri, 13 Dec 2024 04:03:14 GMT
• Title: SMMF: Square-Matricized Momentum Factorization for Memory-Efficient Optimization
• Authors: Kwangryeol Park, Seulki Lee,
• Abstract summary: SMMF is a memory-efficient that reduces the memory requirement of the widely used adaptive learning rate Matrix, such as Adam, by up to 96%. We conduct a regret bound analysis of SMMF, which shows that it converges similarly to non-memory-efficient adaptive learning rate Matrix, such as AdamNC. In our experiment, SMMF takes up to 96% less memory compared to state-of-the-art memory efficients, e.g., Adafactor, CAME, and SM3, while achieving comparable model performance.
• Score: 0.5755004576310332
• License:
• Abstract: We propose SMMF (Square-Matricized Momentum Factorization), a memory-efficient optimizer that reduces the memory requirement of the widely used adaptive learning rate optimizers, such as Adam, by up to 96%. SMMF enables flexible and efficient factorization of an arbitrary rank (shape) of the first and second momentum tensors during optimization, based on the proposed square-matricization and one-time single matrix factorization. From this, it becomes effectively applicable to any rank (shape) of momentum tensors, i.e., bias, matrix, and any rank-d tensors, prevalent in various deep model architectures, such as CNNs (high rank) and Transformers (low rank), in contrast to existing memory-efficient optimizers that applies only to a particular (rank-2) momentum tensor, e.g., linear layers. We conduct a regret bound analysis of SMMF, which shows that it converges similarly to non-memory-efficient adaptive learning rate optimizers, such as AdamNC, providing a theoretical basis for its competitive optimization capability. In our experiment, SMMF takes up to 96% less memory compared to state-of-the-art memory efficient optimizers, e.g., Adafactor, CAME, and SM3, while achieving comparable model performance on various CNN and Transformer tasks.

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