Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning

Armen Aghajanyan, Sonal Gupta, Luke Zettlemoyer


Abstract
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.
Anthology ID:
2021.acl-long.568
Volume:
Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)
Month:
August
Year:
2021
Address:
Online
Venues:
ACL | IJCNLP
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
7319–7328
Language:
URL:
https://aclanthology.org/2021.acl-long.568
DOI:
10.18653/v1/2021.acl-long.568
Award:
 Outstanding Paper
Bibkey:
Cite (ACL):
Armen Aghajanyan, Sonal Gupta, and Luke Zettlemoyer. 2021. Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 7319–7328, Online. Association for Computational Linguistics.
Cite (Informal):
Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning (Aghajanyan et al., ACL 2021)
Copy Citation:
PDF:
https://aclanthology.org/2021.acl-long.568.pdf
Code
 rabeehk/compacter
Data
ANLIGLUEMRPCQuora Question PairsSST