# Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning

arXiv: https://arxiv.org/abs/2012.13255 · HTML: https://mlsanity.com/paper/2012.13255/

## Key facts

- Cited by 671 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2020.

## Built on by (most cited first, 30 of 671)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [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)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [Differentially Private Fine-tuning of Language Models](https://mlsanity.com/paper/2110.06500/) (2021)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (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)
- [Black-Box Tuning for Language-Model-as-a-Service](https://mlsanity.com/paper/2201.03514/) (2022)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [Knowledge Editing for Large Language Models: A Survey](https://mlsanity.com/paper/2310.16218/) (2023)
- [Delta Tuning: A Comprehensive Study of Parameter Efficient Methods for Pre-trained Language Models](https://mlsanity.com/paper/2203.06904/) (2022)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)
- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [How do Large Language Models Handle Multilingualism?](https://mlsanity.com/paper/2402.18815/) (2024)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [AdaMix: Mixture-of-Adaptations for Parameter-efficient Model Tuning](https://mlsanity.com/paper/2210.17451/) (2022)
- [Domain Specialization as the Key to Make Large Language Models Disruptive: A Comprehensive Survey](https://mlsanity.com/paper/2305.18703/) (2023)
- [Evaluating ChatGPT's Information Extraction Capabilities: An Assessment of Performance, Explainability, Calibration, and Faithfulness](https://mlsanity.com/paper/2304.11633/) (2023)
- [ChatEDA: A Large Language Model Powered Autonomous Agent for EDA](https://mlsanity.com/paper/2308.10204/) (2023)
- [A Kernel-Based View of Language Model Fine-Tuning](https://mlsanity.com/paper/2210.05643/) (2022)

## Abstract (arXiv)

Although pretrained language models can be fine-tuned to produce state-of-the-art results for a very wide range of language understanding tasks, the dynamics of this process are not well understood, especially in the low data regime. Why can we use relatively vanilla gradient descent algorithms (e.g., without strong regularization) to tune a model with hundreds of millions of parameters on datasets with only hundreds or thousands of labeled examples? In this paper, we argue that analyzing fine-tuning through the lens of intrinsic dimension provides us with empirical and theoretical intuitions to explain this remarkable phenomenon. We empirically show that common pre-trained models have a very low intrinsic dimension; in other words, there exists a low dimension reparameterization that is as effective for fine-tuning as the full parameter space. For example, by optimizing only 200 trainable parameters randomly projected back into the full space, we can tune a RoBERTa model to achieve 90% of the full parameter performance levels on MRPC. Furthermore, we empirically show that pre-training implicitly minimizes intrinsic dimension and, perhaps surprisingly, larger models tend to have lower intrinsic dimension after a fixed number of pre-training updates, at least in part explaining their extreme effectiveness. Lastly, we connect intrinsic dimensionality with low dimensional task representations and compression based generalization bounds to provide intrinsic-dimension-based generalization bounds that are independent of the full parameter count.