# AltLoRA: Towards Better Gradient Approximation in Low-Rank Adaptation with Alternating Projections

arXiv: https://arxiv.org/abs/2505.12455 · HTML: https://mlsanity.com/paper/2505.12455/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 78 of its 93 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 30 of 78)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)

## Built on by (most cited first, 9 of 9)

- [LoFT: Low-Rank Adaptation That Behaves Like Full Fine-Tuning](https://mlsanity.com/paper/2505.21289/) (2025)
- [Preference-Based Self-Distillation: Beyond KL Matching via Reward Regularization](https://mlsanity.com/paper/2605.05040/) (2026)
- [ADF-LoRA: Alternating Low-Rank Aggregation for Decentralized Federated Fine-Tuning](https://mlsanity.com/paper/2511.18291/) (2025)
- [Train Large, Deploy Compact: Structured Compression for Compact Low-Rank Adaptation](https://mlsanity.com/paper/2510.00192/) (2025)
- [SDS-LoRA: Overcoming Anisotropic Gradient Scaling in Low-Rank Adaptation](https://mlsanity.com/paper/2606.16454/) (2026)
- [Stabilizing Decentralized Federated Fine-Tuning via Topology-Aware Alternating LoRA](https://mlsanity.com/paper/2602.00451/) (2026)
- [ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equations](https://mlsanity.com/paper/2602.07479/) (2026)
- [One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning](https://mlsanity.com/paper/2609.05885/) (2026)
- [DT-LoRA: Reaching Beyond the Tangent Space of Low-Rank Adaptation](https://mlsanity.com/paper/2610.17730/) (2026)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) has emerged as an effective technique for reducing memory overhead in fine-tuning large language models. However, it often suffers from sub-optimal performance compared with full fine-tuning since the update is constrained in the low-rank space. Recent variants such as LoRA-Pro attempt to mitigate this by adjusting the gradients of the low-rank matrices to approximate the full gradient. However, LoRA-Pro's solution is not unique, and different solutions can lead to significantly varying performance in ablation studies. Besides, to incorporate momentum or adaptive optimization design, approaches like LoRA-Pro must first compute the equivalent gradient, causing a higher memory cost close to full fine-tuning. A key challenge remains in integrating momentum properly into the low-rank space with lower memory cost. In this work, we propose AltLoRA, an alternating projection method that avoids the difficulties in gradient approximation brought by the joint update design, meanwhile integrating momentum without higher memory complexity. Our theoretical analysis provides convergence guarantees and further shows that AltLoRA enables stable feature learning and robustness to transformation invariance. Extensive experiments across multiple tasks demonstrate that AltLoRA outperforms LoRA and its variants, narrowing the gap toward full fine-tuning while preserving superior memory efficiency.