# When pre-training hurts LoRA fine-tuning: a dynamical analysis via single-index models

arXiv: https://arxiv.org/abs/2602.02855 · HTML: https://mlsanity.com/paper/2602.02855/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 55 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 30 of 41)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Pre-trained Models for Natural Language Processing: A Survey](https://mlsanity.com/paper/2003.08271/) (2020)
- [Pre-Trained Models: Past, Present and Future](https://mlsanity.com/paper/2106.07139/) (2021)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [Neural Networks can Learn Representations with Gradient Descent](https://mlsanity.com/paper/2206.15144/) (2022)
- [High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation](https://mlsanity.com/paper/2205.01445/) (2022)
- [Online stochastic gradient descent on non-convex losses from high-dimensional inference](https://mlsanity.com/paper/2003.10409/) (2020)
- [Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models](https://mlsanity.com/paper/1708.03395/) (2017)
- [Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup](https://mlsanity.com/paper/1906.08632/) (2019)
- [A high-bias, low-variance introduction to Machine Learning for physicists](https://mlsanity.com/paper/1803.08823/) (2018)
- [The Expressive Power of Low-Rank Adaptation](https://mlsanity.com/paper/2310.17513/) (2023)
- [Multi-digit Number Recognition from Street View Imagery using Deep Convolutional Neural Networks](https://mlsanity.com/paper/1312.6082/) (2013)
- [How Two-Layer Neural Networks Learn, One (Giant) Step at a Time](https://mlsanity.com/paper/2305.18270/) (2023)
- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [Smoothing the Landscape Boosts the Signal for SGD: Optimal Sample Complexity for Learning Single Index Models](https://mlsanity.com/paper/2305.10633/) (2023)
- [Overtrained Language Models Are Harder to Fine-Tune](https://mlsanity.com/paper/2503.19206/) (2025)
- [The Impact of Initialization on LoRA Finetuning Dynamics](https://mlsanity.com/paper/2406.08447/) (2024)
- [The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents](https://mlsanity.com/paper/2402.03220/) (2024)
- [Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks](https://mlsanity.com/paper/2202.00293/) (2022)
- [LoRA Training in the NTK Regime has No Spurious Local Minima](https://mlsanity.com/paper/2402.11867/) (2024)
- [Computational-Statistical Gaps in Gaussian Single-Index Models](https://mlsanity.com/paper/2403.05529/) (2024)
- [From high-dimensional & mean-field dynamics to dimensionless ODEs: A unifying approach to SGD in two-layers networks](https://mlsanity.com/paper/2302.05882/) (2023)
- [Asymptotics of feature learning in two-layer networks after one gradient-step](https://mlsanity.com/paper/2402.04980/) (2024)
- [LoRA-One: One-Step Full Gradient Could Suffice for Fine-Tuning Large Language Models, Provably and Efficiently](https://mlsanity.com/paper/2502.01235/) (2025)
- [Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions](https://mlsanity.com/paper/2405.15459/) (2024)

## Built on by (most cited first, 2 of 2)

- [High-Dimensional Theory of LoRA Fine-Tuning in a Solvable Attention Model](https://mlsanity.com/paper/2606.05899/) (2026)
- [A Dynamical Theory of LoRA in Continual Learning](https://mlsanity.com/paper/2609.39367/) (2026)

## Abstract (arXiv)

Pre-training on a source task is usually expected to facilitate fine-tuning on similar downstream problems. In this work, we mathematically show that this naive intuition is not always true: excessive pre-training can computationally slow down fine-tuning optimization. We study this phenomenon for low-rank adaptation (LoRA) fine-tuning on single-index models trained under one-pass SGD. Leveraging a summary statistics description of the fine-tuning dynamics, we precisely characterize how the convergence rate depends on the initial fine-tuning alignment and the degree of non-linearity of the target task. The key take away is that even when the pre-training and downstream tasks are well aligned, strong pre-training can induce a prolonged search phase and hinder convergence. Our theory thus provides a unified picture of how pre-training strength and task difficulty jointly shape the dynamics and limitations of LoRA fine-tuning in a nontrivial tractable model. On the practical side, we empirically show that our theoretical findings extend beyond our toy model and remain relevant in the context of a vision-transformer model trained on real data.