Adapprox: Adaptive Approximation in Adam Optimization via Randomized Low-Rank Matrices

TL;DR

Adapprox introduces a memory-efficient Adam optimizer variant using randomized low-rank matrix approximation with adaptive rank selection, improving memory savings, convergence speed, and downstream task performance in large-scale deep learning.

Contribution

It presents a novel adaptive low-rank approximation method for Adam's second moment, balancing accuracy and memory efficiency with optional guidance strategies.

Findings

Achieves 34.5% to 49.9% memory savings on GPT-2 models

Enhances convergence speed compared to AdamW

Improves downstream task performance

Abstract

As deep learning models exponentially increase in size, optimizers such as Adam encounter significant memory consumption challenges due to the storage of first and second moment data. Current memory-efficient methods like Adafactor and CAME often compromise accuracy with their matrix factorization techniques. Addressing this, we introduce Adapprox, a novel approach that employs randomized low-rank matrix approximation for a more effective and accurate approximation of Adam's second moment. Adapprox features an adaptive rank selection mechanism, finely balancing accuracy and memory efficiency, and includes an optional cosine similarity guidance strategy to enhance stability and expedite convergence. In GPT-2 training and downstream tasks, Adapprox surpasses AdamW by achieving 34.5% to 49.9% and 33.8% to 49.9% memory savings for the 117M and 345M models, respectively, with the first moment enabled, and further increases these savings without the first moment. Besides, it enhances convergence speed and improves downstream task performance relative to its counterparts.