Towards Efficient Optimizer Design for LLM via Structured Fisher Approximation with a Low-Rank Extension

• URL: http://arxiv.org/abs/2502.07752v2
• Date: Thu, 20 Feb 2025 18:48:58 GMT
• Title: Towards Efficient Optimizer Design for LLM via Structured Fisher Approximation with a Low-Rank Extension
• Authors: Wenbo Gong, Meyer Scetbon, Chao Ma, Edward Meeds,
• Abstract summary: This paper makes a step towards the systematic design of efficient approximations through the lens of Fisher information matrix (FIM) We show that many state-of-the-art efficient approximations can be viewed as solutions to FIM (under the Frobenius norm) with specific structural assumptions. We propose two design recommendations of practical efficients for LLMs, involving careful selection of structural assumptions to balance generality and efficiency.
• Score: 16.037614012166063
• License:
• Abstract: Designing efficient optimizers for large language models (LLMs) with low-memory requirements and fast convergence is an important and challenging problem. This paper makes a step towards the systematic design of such optimizers through the lens of structured Fisher information matrix (FIM) approximation. We show that many state-of-the-art efficient optimizers can be viewed as solutions to FIM approximation (under the Frobenius norm) with specific structural assumptions. Building on these insights, we propose two design recommendations of practical efficient optimizers for LLMs, involving the careful selection of structural assumptions to balance generality and efficiency, and enhancing memory efficiency of optimizers with general structures through a novel low-rank extension framework. We demonstrate how to use each design approach by deriving new memory-efficient optimizers: Row and Column Scaled SGD (RACS) and Adaptive low-dimensional subspace estimation (Alice). Experiments on LLaMA pre-training (up to 1B parameters) validate the effectiveness, showing faster and better convergence than existing memory-efficient baselines and Adam with little memory overhead. Notably, Alice achieves better than 2x faster convergence over Adam, while RACS delivers strong performance on the 1B model with SGD-like memory.

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