# Understanding Catastrophic Forgetting In LoRA via Mean-Field Attention Dynamics

arXiv: https://arxiv.org/abs/2402.15415 · HTML: https://mlsanity.com/paper/2402.15415/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 62 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [A mathematical perspective on Transformers](https://mlsanity.com/paper/2312.10794/) (2023)
- [Stabilizing Transformer Training by Preventing Attention Entropy Collapse](https://mlsanity.com/paper/2303.06296/) (2023)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [The emergence of clusters in self-attention dynamics](https://mlsanity.com/paper/2305.05465/) (2023)
- [Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View](https://mlsanity.com/paper/1906.02762/) (2019)
- [Rank Diminishing in Deep Neural Networks](https://mlsanity.com/paper/2206.06072/) (2022)
- [The Shaped Transformer: Attention Models in the Infinite Depth-and-Width Limit](https://mlsanity.com/paper/2306.17759/) (2023)
- [A Mathematical Theory of Attention](https://mlsanity.com/paper/2007.02876/) (2020)
- [Self-attention Networks Localize When QK-eigenspectrum Concentrates](https://mlsanity.com/paper/2402.02098/) (2024)
- [A Functional Perspective on Learning Symmetric Functions with Neural Networks](https://mlsanity.com/paper/2008.06952/) (2020)
- [Are More Layers Beneficial to Graph Transformers?](https://mlsanity.com/paper/2303.00579/) (2023)
- [Stochastic Deep Networks](https://mlsanity.com/paper/1811.07429/) (2018)
- [On the impact of activation and normalization in obtaining isometric embeddings at initialization](https://mlsanity.com/paper/2305.18399/) (2023)

## Built on by (most cited first, 7 of 7)

- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [Dynamic metastability in the self-attention model](https://mlsanity.com/paper/2410.06833/) (2024)
- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [Synchronization of mean-field models on the circle](https://mlsanity.com/paper/2507.22857/) (2025)
- [Does Low Rank Adaptation Lead to Lower Robustness against Training-Time Attacks?](https://mlsanity.com/paper/2505.12871/) (2025)
- [The Intruder Threshold: A Spectral Law for LoRA Fine-Tuning](https://mlsanity.com/paper/2607.23711/) (2026)
- [Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers](https://mlsanity.com/paper/2605.07772/) (2026)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) is the dominant parameter-efficient fine-tuning method due to its favorable compute-performance trade-off, yet it suffers from catastrophic forgetting. We study forgetting through a tractable _mean-field self-attention_ toy model, where tokens evolve as an interacting particle system and LoRA acts as a low-rank perturbation. Using tools from partial differential equations and dynamical systems, we characterize regimes suggesting a phase transition between forgetting and non-forgetting behavior. We show that one phase transition appears with respect to the norm of the perturbation, and the other with respect to the depth of the Transformers. We further bound the time-to-deviation in terms of the perturbation size and spectral quantities, and corroborate the predicted trends with experiments and exploratory analyses on real models under LoRA fine-tuning.