We introduce APOLLO (Approximated Gradient Scaling for Memory Efficient LLM Optimization), a novel method designed to optimize the memory efficiency of training large language models (LLM), offering SGD-like memory cost while delivering AdamW-level performance for pre-training!
APOLLO effectively integrates two major ideas for memory-efficient LLM training: low-rank approximation (GaLore) and optimizer state redundancy reduction (Adam-mini). However, APOLLO takes memory efficiency to a new level, achieving significant memory savings (below GaLore and its variants, and close to SGD) while maintaining or surpassing the performance of Adam(W).
Our key contributions include:
-
Structured Learning Rate Updates for LLM Training: We identify that structured learning rate updates, such as channel-wise or tensor-wise scaling, are sufficient for LLM training. This approach explores redundancy in AdamW's element-wise learning rate update rule, forming a basis for our APOLLO method.
-
Approximated Channel-wise Gradient Scaling in a Low-Rank Auxiliary Space (APOLLO):
APOLLO proposes a practical and memory-efficient method to approximate channel-wise gradient scaling factors in an auxiliary low-rank space using pure random projections. This method achieves superior performance compared to AdamW, even with lower-rank approximations, while maintaining excellent memory efficiency. -
Minimal-Rank Tensor-wise Gradient Scaling (APOLLO-Mini):
APOLLO-Mini introduces extreme memory efficiency by applying tensor-wise gradient scaling using only a rank-1 auxiliary sub-space. This results in SGD-level memory costs while outperforming AdamW, showcasing the effectiveness of the approach.
Figure 1: The APOLLO Framework for Memory-Efficient LLM Training. The channel-wise or tensor-wise gradient scaling factor is obtained via an auxiliary low-rank optimizer state, constructed using pure random projection (no SVD required).
Figure 2: System Benefits of APOLLO for Pre-training LLaMA 7B. (left): Memory breakdown comparison for a single batch size; (right): End-to-end training throughput on 8 A100-80GB GPUs
- Offical APOLLO release is on the way
- APOLLO combined with int8 weight quantization from Q-Galore
- [2024/12] APOLLO validated by third-party Julia implementation!: Our APOLLO optimizer has been independently validated by a third party using a Julia implementation. Check out the post. They are also working to integrate APOLLO into FluxML.
- [2024/12] Unofficial Implementation Available!: For a quick try-out, please check out the Unofficial Implementation implemented by third-party contributors and validated by us.
- [2024/12] APOLLO Paper Released: Our paper is now available on arXiv! Check it out here: [Paper].
Large language models (LLMs) demonstrate remarkable capabilities but are notoriously memory-intensive during training, particularly with the popular Adam optimizer. This memory burden often necessitates using more GPUs, smaller batch sizes, or high-end hardware, thereby limiting scalability and training efficiency. To address this, various memory-efficient optimizers have been proposed to reduce optimizer memory usage. However, they face key challenges: (i) reliance on costly SVD operations (e.g., GaLore, Fira); (ii) significant performance trade-offs compared to AdamW (e.g., Flora); and (iii) still substantial memory overhead of optimization states in order to maintain competitive performance (e.g., 1/4 rank in Galore, and full-rank first momentum in Adam-mini).
In this work, we investigate the redundancy in Adam's learning rate adaption rule and identify that it can be coarsened as a structured learning rate update (channel-wise or tensor-wise). Based on this insight, we propose a novel approach, Approximated Gradient Scaling for Memory Efficient LLM Optimization (APOLLO), which approximate the channel-wise learning rate scaling with an auxiliary low-rank optimizer state based on pure random projection. The structured learning rate update rule makes APOLLO highly tolerant to further memory reduction with lower rank, halving the rank while delivering similar pre-training performance. We further propose an extreme memory-efficient version, APOLLO-mini, which utilizes tensor-wise scaling with only a rank-1 auxiliary sub-space, achieving SGD-level memory cost but superior pre-training performance than Adam(W).
We conduct extensive experiments across different tasks and model architectures, showing that APOLLO series performs generally on-par with, or even better than Adam(W). Meanwhile, APOLLO achieves even greater memory savings than Galore, by almost eliminating the optimization states in AdamW. These savings translate into significant system benefits:
- Enhanced Throughput: APOLLO and APOLLO-mini achieve up to 3x throughput on a 4xA100-80GB setup compared to Adam by fully utilizing memory to support 4x larger batch sizes.
- Improved Model Scalability: APOLLO-mini for the first time enables pre-training LLaMA-13B model with naive DDP on A100-80G without requiring other system-level optimizations
- Low-End GPU Pre-training: Combined with quantization, the APOLLO series for the first time enables the training of LLaMA-7B from scratch using less than 12 GB of memory.
For questions or collaboration inquiries, feel free to reach out our core contributors:
- 📧 Email: hqzhu@utexas.edu
- 📧 Email: zhenyu.zhang@utexas.edu
If you find APOLLO useful in your work, please consider citing our paper:
@misc{zhu2024apollosgdlikememoryadamwlevel,
title={APOLLO: SGD-like Memory, AdamW-level Performance},
author={Hanqing Zhu and Zhenyu Zhang and Wenyan Cong and Xi Liu and Sem Park and Vikas Chandra and Bo Long and David Z. Pan and Zhangyang Wang and Jinwon Lee},
year={2024},
eprint={2412.05270},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2412.05270},
}
