# AdaLomo: Low-memory Optimization with Adaptive Learning Rate

arXiv: https://arxiv.org/abs/2310.10195 · HTML: https://mlsanity.com/paper/2310.10195/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Black-Box Tuning for Language-Model-as-a-Service](https://mlsanity.com/paper/2201.03514/) (2022)
- [The Lipschitz Constant of Self-Attention](https://mlsanity.com/paper/2006.04710/) (2020)
- [Full Parameter Fine-tuning for Large Language Models with Limited Resources](https://mlsanity.com/paper/2306.09782/) (2023)

## Built on by (most cited first, 30 of 31)

- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [Fira: Can We Achieve Full-rank Training of LLMs Under Low-rank Constraint?](https://mlsanity.com/paper/2410.01623/) (2024)
- [Q-GaLore: Quantized GaLore with INT4 Projection and Layer-Adaptive Low-Rank Gradients](https://mlsanity.com/paper/2407.08296/) (2024)
- [LDAdam: Adaptive Optimization from Low-Dimensional Gradient Statistics](https://mlsanity.com/paper/2410.16103/) (2024)
- [Weak-to-Strong Reasoning](https://mlsanity.com/paper/2407.13647/) (2024)
- [Multi-Layer Transformers Gradient Can be Approximated in Almost Linear Time](https://mlsanity.com/paper/2408.13233/) (2024)
- [SUMO: Subspace-Aware Moment-Orthogonalization for Accelerating Memory-Efficient LLM Training](https://mlsanity.com/paper/2505.24749/) (2025)
- [Grass: Compute Efficient Low-Memory LLM Training with Structured Sparse Gradients](https://mlsanity.com/paper/2406.17660/) (2024)
- [AdaRankGrad: Adaptive Gradient-Rank and Moments for Memory-Efficient LLMs Training and Fine-Tuning](https://mlsanity.com/paper/2410.17881/) (2024)
- [GaLore 2: Large-Scale LLM Pre-Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2504.20437/) (2025)
- [GoRA: Gradient-driven Adaptive Low Rank Adaptation](https://mlsanity.com/paper/2502.12171/) (2025)
- [Slamming: Training a Speech Language Model on One GPU in a Day](https://mlsanity.com/paper/2502.15814/) (2025)
- [Reflecting on the State of Rehearsal-free Continual Learning with Pretrained Models](https://mlsanity.com/paper/2406.09384/) (2024)
- [Mini-Sequence Transformer: Optimizing Intermediate Memory for Long Sequences Training](https://mlsanity.com/paper/2407.15892/) (2024)
- [AdamS: Momentum Itself Can Be A Normalizer for LLM Pretraining and Post-training](https://mlsanity.com/paper/2505.16363/) (2025)
- [LORENZA: Enhancing Generalization in Low-Rank Gradient LLM Training via Efficient Zeroth-Order Adaptive SAM](https://mlsanity.com/paper/2502.19571/) (2025)
- [FlashOptim: Optimizers for Memory-Efficient Training](https://mlsanity.com/paper/2602.23349/) (2026)
- [Achieving Peak Performance for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2409.04833/) (2024)
- [Low-rank Momentum Factorization for Memory Efficient Training](https://mlsanity.com/paper/2507.08091/) (2025)
- [CoLLiE: Collaborative Training of Large Language Models in an Efficient Way](https://mlsanity.com/paper/2312.00407/) (2023)
- [OLion: Approaching the Hadamard Ideal by Intersecting Spectral and ℓ∞ Implicit Biases](https://mlsanity.com/paper/2602.01105/) (2026)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)
- [MISA: Memory-Efficient LLMs Optimization with Module-wise Importance Sampling](https://mlsanity.com/paper/2511.00056/) (2025)
- [MGUP: A Momentum-Gradient Alignment Update Policy for Stochastic Optimization](https://mlsanity.com/paper/2606.17526/) (2026)
- [FORGE: Fused On-Register Gradient Elimination for Memory-Efficient LLM Training](https://mlsanity.com/paper/2606.22932/) (2026)
- [MLorc: Momentum Low-rank Compression for Memory Efficient Large Language Model Adaptation](https://mlsanity.com/paper/2506.01897/) (2025)
- [LoSiA: Efficient High-Rank Fine-Tuning via Subnet Localization and Optimization](https://mlsanity.com/paper/2507.04487/) (2025)
- [Backward-Friendly Optimization: Training Large Language Models with Approximate Gradients under Memory Constraints](https://mlsanity.com/paper/2510.22467/) (2025)

## Abstract (arXiv)

Large language models have achieved remarkable success, but their extensive parameter size necessitates substantial memory for training, thereby setting a high threshold. While the recently proposed low-memory optimization (LOMO) reduces memory footprint, its optimization technique, akin to stochastic gradient descent, is sensitive to hyper-parameters and exhibits suboptimal convergence, failing to match the performance of the prevailing optimizer for large language models, AdamW. Through empirical analysis of the Adam optimizer, we found that, compared to momentum, the adaptive learning rate is more critical for bridging the gap. Building on this insight, we introduce the low-memory optimization with adaptive learning rate (AdaLomo), which offers an adaptive learning rate for each parameter. To maintain memory efficiency, we employ non-negative matrix factorization for the second-order moment estimation in the optimizer state. Additionally, we suggest the use of a grouped update normalization to stabilize convergence. Our experiments with instruction-tuning and further pre-training demonstrate that AdaLomo achieves results on par with AdamW, while significantly reducing memory requirements, thereby lowering the hardware barrier to training large language models. The code is accessible at https://github.com/OpenLMLab/LOMO.