# APOLLO: SGD-like Memory, AdamW-level Performance

arXiv: https://arxiv.org/abs/2412.05270 · HTML: https://mlsanity.com/paper/2412.05270/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 51 references that are in the map.
- First posted on arXiv 6 Dec 2024.

## Builds on (most cited first, 30 of 39)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [MobileLLM: Optimizing Sub-billion Parameter Language Models for On-Device Use Cases](https://mlsanity.com/paper/2402.14905/) (2024)
- [ChatGPT: Jack of all trades, master of none](https://mlsanity.com/paper/2302.10724/) (2023)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [More ConvNets in the 2020s: Scaling up Kernels Beyond 51x51 using Sparsity](https://mlsanity.com/paper/2207.03620/) (2022)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [Full Parameter Fine-tuning for Large Language Models with Limited Resources](https://mlsanity.com/paper/2306.09782/) (2023)
- [Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning](https://mlsanity.com/paper/2010.05627/) (2020)
- [Improving Generalization Performance by Switching from Adam to SGD](https://mlsanity.com/paper/1712.07628/) (2017)
- [Why Transformers Need Adam: A Hessian Perspective](https://mlsanity.com/paper/2402.16788/) (2024)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Compressing LLMs: The Truth is Rarely Pure and Never Simple](https://mlsanity.com/paper/2310.01382/) (2023)
- [Toward Understanding Why Adam Converges Faster Than SGD for Transformers](https://mlsanity.com/paper/2306.00204/) (2023)
- [Fira: Can We Achieve Full-rank Training of LLMs Under Low-rank Constraint?](https://mlsanity.com/paper/2410.01623/) (2024)

## Built on by (most cited first, 30 of 54)

- [ASGO: Adaptive Structured Gradient Optimization](https://mlsanity.com/paper/2503.20762/) (2025)
- [The Path Not Taken: RLVR Provably Learns Off the Principals](https://mlsanity.com/paper/2511.08567/) (2025)
- [CoLA: Compute-Efficient Pre-Training of LLMs via Low-Rank Activation](https://mlsanity.com/paper/2502.10940/) (2025)
- [SWAN: SGD with Normalization and Whitening Enables Stateless LLM Training](https://mlsanity.com/paper/2412.13148/) (2024)
- [SUMO: Subspace-Aware Moment-Orthogonalization for Accelerating Memory-Efficient LLM Training](https://mlsanity.com/paper/2505.24749/) (2025)
- [Forget What You Know about LLMs Evaluations -- LLMs are Like a Chameleon](https://mlsanity.com/paper/2502.07445/) (2025)
- [Memory-Efficient LLM Pretraining via Minimalist Optimizer Design](https://mlsanity.com/paper/2506.16659/) (2025)
- [LOST: Low-rank and Sparse Pre-training for Large Language Models](https://mlsanity.com/paper/2508.02668/) (2025)
- [Gradient Multi-Normalization for Stateless and Scalable LLM Training](https://mlsanity.com/paper/2502.06742/) (2025)
- [GradPower: Powering Gradients for Faster Language Model Pre-Training](https://mlsanity.com/paper/2505.24275/) (2025)
- [E3D-Bench: A Benchmark for End-to-End 3D Geometric Foundation Models](https://mlsanity.com/paper/2506.01933/) (2025)
- [CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structure](https://mlsanity.com/paper/2509.18993/) (2025)
- [On Surprising Effectiveness of Masking Updates in Adaptive Optimizers](https://mlsanity.com/paper/2602.15322/) (2026)
- [CE-LoRA: Computation-Efficient LoRA Fine-Tuning for Language Models](https://mlsanity.com/paper/2502.01378/) (2025)
- [Fast Catch-Up, Late Switching: Optimal Batch Size Scheduling via Functional Scaling Laws](https://mlsanity.com/paper/2602.14208/) (2026)
- [Position: Weight Space Should Be a First-Class Generative AI Modality](https://mlsanity.com/paper/2605.18632/) (2026)
- [Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarking](https://mlsanity.com/paper/2505.22922/) (2025)
- [Conda: Column-Normalized Adam for Training Large Language Models Faster](https://mlsanity.com/paper/2509.24218/) (2025)
- [FlashOptim: Optimizers for Memory-Efficient Training](https://mlsanity.com/paper/2602.23349/) (2026)
- [POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation](https://mlsanity.com/paper/2603.05500/) (2026)
- [Low-rank Momentum Factorization for Memory Efficient Training](https://mlsanity.com/paper/2507.08091/) (2025)
- [DACTYL: Diverse Adversarial Corpus of Texts Yielded from Large Language Models](https://mlsanity.com/paper/2508.00619/) (2025)
- [Taming LLMs by Scaling Learning Rates with Gradient Grouping](https://mlsanity.com/paper/2506.01049/) (2025)
- [Memory-Efficient Fine-Tuning via Low-Rank Activation Compression](https://mlsanity.com/paper/2509.23472/) (2025)
- [BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Models](https://mlsanity.com/paper/2512.12131/) (2025)
- [Train Less, Infer Faster: Efficient Model Finetuning and Compression via Structured Sparsity](https://mlsanity.com/paper/2602.09169/) (2026)
- [Navigating LLM Valley: From AdamW to Memory-Efficient and Matrix-Based Optimizers](https://mlsanity.com/paper/2605.09176/) (2026)
- [FORGE: Fused On-Register Gradient Elimination for Memory-Efficient LLM Training](https://mlsanity.com/paper/2606.22932/) (2026)
- [ISO: An RLVR-Native Optimization Stack](https://mlsanity.com/paper/2607.19331/) (2026)
- [GWT: Scalable Optimizer State Compression for Large Language Model Training](https://mlsanity.com/paper/2501.07237/) (2025)

## Abstract (arXiv)

Large language models (LLMs) are notoriously memory-intensive during training, particularly with the popular AdamW optimizer. This memory burden necessitates using more or higher-end GPUs or reducing batch sizes, limiting training scalability and throughput. To address this, various memory-efficient optimizers have been proposed to reduce optimizer memory usage. However, they face critical challenges: (i) reliance on costly SVD operations; (ii) significant performance trade-offs compared to AdamW; and (iii) still substantial optimizer memory overhead to maintain competitive performance. In this work, we identify that AdamW's learning rate adaptation rule can be effectively coarsened as a structured learning rate update. Based on this insight, we propose Approximated Gradient Scaling for Memory-Efficient LLM Optimization (APOLLO), which approximates learning rate scaling using an auxiliary low-rank optimizer state based on pure random projection. This structured learning rate update rule makes APOLLO highly tolerant to further memory reductions while delivering comparable pre-training performance. Even its rank-1 variant, APOLLO-Mini, achieves superior pre-training performance compared to AdamW with SGD-level memory costs. Extensive experiments demonstrate that the APOLLO series performs on-par with or better than AdamW, while achieving greater memory savings by nearly eliminating the optimization states of AdamW. These savings provide significant system-level benefits: (1) Enhanced Throughput: 3x throughput on an 8xA100-80GB setup compared to AdamW by supporting 4x larger batch sizes. (2) Improved Model Scalability: Pre-training LLaMA-13B with naive DDP on A100-80GB GPUs without system-level optimizations. (3) Low-End GPU Friendly Pre-training: Pre-training LLaMA-7B on a single GPU using less than 12 GB of memory with weight quantization.