# Scaling Laws for Forgetting When Fine-Tuning Large Language Models

arXiv: https://arxiv.org/abs/2401.05605 · HTML: https://mlsanity.com/paper/2401.05605/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 11 Jan 2024.

## Builds on (most cited first, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [Unified Scaling Laws for Routed Language Models](https://mlsanity.com/paper/2202.01169/) (2022)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Selective Experience Replay for Lifelong Learning](https://mlsanity.com/paper/1802.10269/) (2018)
- [Reinforced Continual Learning](https://mlsanity.com/paper/1805.12369/) (2018)
- [Delta Tuning: A Comprehensive Study of Parameter Efficient Methods for Pre-trained Language Models](https://mlsanity.com/paper/2203.06904/) (2022)
- [Uncertainty-based Continual Learning with Adaptive Regularization](https://mlsanity.com/paper/1905.11614/) (2019)
- [Mixout: Effective Regularization to Finetune Large-scale Pretrained Language Models](https://mlsanity.com/paper/1909.11299/) (2019)

## Built on by (most cited first, 30 of 38)

- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [Large Scale Transfer Learning for Tabular Data via Language Modeling](https://mlsanity.com/paper/2406.12031/) (2024)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Scaling Laws for Forgetting during Finetuning with Pretraining Data Injection](https://mlsanity.com/paper/2502.06042/) (2025)
- [Efficient Prediction of Pass@k Scaling in Large Language Models](https://mlsanity.com/paper/2510.05197/) (2025)
- [Human-inspired Perspectives: A Survey on AI Long-term Memory](https://mlsanity.com/paper/2411.00489/) (2024)
- [TeamLoRA: Boosting Low-Rank Adaptation with Expert Collaboration and Competition](https://mlsanity.com/paper/2408.09856/) (2024)
- [Aegis: Taxonomy and Optimizations for Overcoming Agent-Environment Failures in LLM Agents](https://mlsanity.com/paper/2508.19504/) (2025)
- [Demystifying Language Model Forgetting with Low-rank Example Associations](https://mlsanity.com/paper/2406.14026/) (2024)
- [Can Muon Fine-tune Adam-Pretrained Models?](https://mlsanity.com/paper/2605.10468/) (2026)
- [Learning, Fast and Slow: Towards LLMs That Adapt Continually](https://mlsanity.com/paper/2605.12484/) (2026)
- [The Devil in the Details: Emergent Misalignment, Format and Coherence in Open-Weights LLMs](https://mlsanity.com/paper/2511.20104/) (2025)
- [Fine-tuning Large Language Models with Limited Data: A Survey and Practical Guide](https://mlsanity.com/paper/2411.09539/) (2024)
- [A Comparative Analysis of LLM Adaptation: SFT, LoRA, and ICL in Data-Scarce Scenarios](https://mlsanity.com/paper/2511.00130/) (2025)
- [Improving Rule-based Reasoning in LLMs using Neurosymbolic Representations](https://mlsanity.com/paper/2502.01657/) (2025)
- [MixSD: Mixed Contextual Self-Distillation for Knowledge Injection](https://mlsanity.com/paper/2605.16865/) (2026)
- [MemSFT: Mitigating Alignment Tax with an External Parametric Memory](https://mlsanity.com/paper/2607.25614/) (2026)
- [Evaluating the Robustness of Chinchilla Compute-Optimal Scaling](https://mlsanity.com/paper/2509.23963/) (2025)
- [Least but not Last: Fine-tuning Intermediate Principal Components for Better Performance-Forgetting Trade-Offs](https://mlsanity.com/paper/2602.03493/) (2026)
- [Fine-tuning MLLMs Without Forgetting Is Easier Than You Think](https://mlsanity.com/paper/2603.14493/) (2026)
- [The Intruder Threshold: A Spectral Law for LoRA Fine-Tuning](https://mlsanity.com/paper/2607.23711/) (2026)
- [Fine-Tuning Without Forgetting via Loss-Adaptive Learning Rates](https://mlsanity.com/paper/2605.20005/) (2026)
- [The Future of Facts: Tracing the Factual Generation-Verification Gap](https://mlsanity.com/paper/2605.27564/) (2026)
- [AILoRA: Function-Aware Asymmetric Initialization for Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2510.08034/) (2025)
- [R2R: A Route-to-Rerank Post-Training Framework for Multi-Domain Decoder-Only Rerankers](https://mlsanity.com/paper/2511.19987/) (2025)
- [SignRoundV2: Toward Closing the Performance Gap in Extremely Low-Bit Post-Training Quantization for LLMs](https://mlsanity.com/paper/2512.04746/) (2025)
- [CureAgent: A Training-Free Executor-Analyst Framework for Clinical Reasoning](https://mlsanity.com/paper/2512.05576/) (2025)
- [PLATE: Plasticity-Tunable Efficient Adapters for Geometry-Aware Continual Learning](https://mlsanity.com/paper/2602.03846/) (2026)
- [Awakening the Sleeping Agent: Lean-Specific Agentic Data Reactivates General Tool Use in Goedel Prover](https://mlsanity.com/paper/2604.08388/) (2026)

## Abstract (arXiv)

We study and quantify the problem of forgetting when fine-tuning pre-trained large language models (LLMs) on a downstream task. We find that parameter-efficient fine-tuning (PEFT) strategies, such as Low-Rank Adapters (LoRA), still suffer from catastrophic forgetting. In particular, we identify a strong inverse linear relationship between the fine-tuning performance and the amount of forgetting when fine-tuning LLMs with LoRA. We further obtain precise scaling laws that show forgetting increases as a shifted power law in the number of parameters fine-tuned and the number of update steps. We also examine the impact of forgetting on knowledge, reasoning, and the safety guardrails trained into Llama 2 7B chat. Our study suggests that forgetting cannot be avoided through early stopping or by varying the number of parameters fine-tuned. We believe this opens up an important safety-critical direction for future research to evaluate and develop fine-tuning schemes which mitigate forgetting