Adam-mini: Use Fewer Learning Rates To Gain More

We propose Adam-mini, an optimizer that achieves on-par or better performance than AdamW with 45% to 50% less memory footprint. Adam-mini reduces memory by cutting down the learning rate resources in Adam (i.e., 1/ √ v). We find that ≥ 90% of these learning rates in v could be harmlessly removed if we (1) carefully partition the parameters into blocks following our proposed principle on Hessian structure; (2) assign a single but good learning rate to each parameter block. We further find that, for each of these parameter blocks, there exists a single high-quality learning rate that can outperform Adam, provided that sufficient resources are available to search it out. We then provide one cost-effective way to find good learning rates and propose Adammini. Empirically, we verify that Adam-mini performs on par or better than AdamW on various language models sized from 125M to 7B for pretraining, supervised fine-tuning, and RLHF. The reduced memory footprint of Adam-mini also alleviates communication overheads among GPUs, thereby increasing throughput. For instance, Adam-mini achieves 49.6% higher throughput than AdamW when pre-training Llama2-7B on 2× A800-80GB GPUs, which saves 33% wallclock time for pre-training. Our implementation of Adam-mini is available at https:// github.com/zyushun/Adam-mini .