# Theoretical Insights into Fine-Tuning Attention Mechanism: Generalization and Optimization

arXiv: https://arxiv.org/abs/2410.02247 · HTML: https://mlsanity.com/paper/2410.02247/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 52 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [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)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [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)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Deep Information Propagation](https://mlsanity.com/paper/1611.01232/) (2016)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)
- [Noisy Channel Language Model Prompting for Few-Shot Text Classification](https://mlsanity.com/paper/2108.04106/) (2021)
- [Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation](https://mlsanity.com/paper/1902.04760/) (2019)
- [Reasoning About Generalization via Conditional Mutual Information](https://mlsanity.com/paper/2001.09122/) (2020)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [On the Impact of the Activation Function on Deep Neural Networks Training](https://mlsanity.com/paper/1902.06853/) (2019)
- [Scan and Snap: Understanding Training Dynamics and Token Composition in 1-layer Transformer](https://mlsanity.com/paper/2305.16380/) (2023)

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

- [Put the Space of LoRA Initialization to the Extreme to Preserve Pre-trained Knowledge](https://mlsanity.com/paper/2503.02659/) (2025)
- [Cognitive Edge Computing: A Comprehensive Survey on Optimizing Large Models and AI Agents for Pervasive Deployment](https://mlsanity.com/paper/2501.03265/) (2025)
- [Compositional Generalization from Learned Skills via CoT Training: A Theoretical and Structural Analysis for Reasoning](https://mlsanity.com/paper/2502.04667/) (2025)
- [Layer-wise dynamic rank for compressing large language models](https://mlsanity.com/paper/2509.25622/) (2025)
- [Simulate, Refocus and Ensemble: An Attention-Refocusing Scheme for Domain Generalization](https://mlsanity.com/paper/2507.12851/) (2025)
- [Parameter Importance-Driven Continual Learning for Foundation Models](https://mlsanity.com/paper/2511.15375/) (2025)
- [Boosting Long-Context Management via Query-Guided Activation Refilling](https://mlsanity.com/paper/2412.12486/) (2024)
- [Fine-Tuning Without Forgetting In-Context Learning: A Theoretical Analysis of Linear Attention Models](https://mlsanity.com/paper/2602.23197/) (2026)
- [GradES: Significantly Faster Training in Transformers with Gradient-Based Early Stopping](https://mlsanity.com/paper/2509.01842/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs), built on Transformer architectures, exhibit remarkable generalization across a wide range of tasks. However, fine-tuning these models for specific tasks remains resource-intensive due to their extensive parameterization. In this paper, we explore two remarkable phenomena related to the attention mechanism during the fine-tuning of LLMs (where Wq, Wk, and Wv denote the weights of the query, key, and value layers, respectively). The first phenomenon, termed "Unequal Importance of Attention Matrices", highlights the impact of fine-tuning different weight matrices. It shows that optimizing the Wv matrix yields significantly better performance than optimizing the Wk matrix. Fine-tuning only the Wq and Wv matrices is computationally efficient while delivering results comparable to, or even better than fine-tuning all three matrices (Wq, Wk, and Wv). The second phenomenon,"Attention Matrices with Customized Learning Rate Lead to Better Convergence", emphasizes the importance of assigning distinct learning rates to these matrices. Specifically, a higher learning rate for the Wv matrix compared to Wq and Wk accelerates convergence and improves performance. Building on these insights, we propose a new strategy that improves fine-tuning efficiency in terms of both storage and time. Experimental results on benchmark datasets validate the effectiveness of this approach, supporting our theoretical findings. Our analysis lays the theoretical groundwork for configuring and improving algorithms in LLMs fine-tuning.