Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning

By Armen Aghajanyan, Luke S. Zettlemoyer, Sonal Gupta. 2020

936 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Large Language Models

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Citations in the corpus

Prefix-Tuning: Optimizing Continuous Prompts for Generation (2021, background): “Recent work by Aghajanyan et al. (2020) uses intrinsic dimension to show that there exists a lowdimensional reparameterization that is as effective for fine-tuning as the full parametrization.”
LoRA: Low-Rank Adaptation of Large Language Models (2021, background): “We take inspiration from [1, 20] which show that the learned over-parametrized models in fact reside on a low intrinsic dimension.”
Compacter: Efficient Low-Rank Hypercomplex Adapter Layers (2021, methodology): “The theoretically motivated low-rank methods train a small number of parameters that lie in a low-dimensional subspace using random projections [13, 14].”
Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning (2022, methodology): “Specifically, we compare with 9 strong PEFT methods: BitFit [47] which updates only the bias parameters; Adapters [23] which introduce task-specific layers after the self-attention and position-wise feed-forward networks; Compacter and Compacter++ [28] which improve upon adapters by using low-rank m”
Prompt-free and Efficient Few-shot Learning with Language Models (2022, methodology): “, 2021) and low-rank methods (Li et al., 2018; Aghajanyan et al., 2021), as an efficient fine-tuning method for PLMs.”
Adding Conditional Control to Text-to-Image Diffusion Models (2023, background): “Low-Rank Adaptation (LoRA) prevents catastrophic forgetting [31] by learning the offset of parameters with low-rank matrices, based on the observation that many over-3837 parameterized models reside in a low intrinsic dimension subspace [2, 47].”
Black-Box Tuning for Language-Model-as-a-Service (2022, methodology): “It has been demonstrated that optimizing only hundreds (Aghajanyan et al., 2021) or even dozens (Qin et al., 2021) of parameters can achieve non-trivial performance.”
DyLoRA: Parameter-Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation (2022, background): “It has been shown in (Aghajanyan et al., 2020) that for classiﬁcation tasks such as natural language understanding (NLU), PLMs have a low intrinsic dimension.”
PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models (2024, neutral): “PEFT encompasses strategies like partial fine-tuning [15, 16, 17, 18, 19, 20, 21, 22], soft prompt fine-tuning [23, 24, 25, 26, 27, 28, 29], non-linear adapter fine-tuning [30, 31, 32, 33, 34, 35, 36, 37, 38, 39], and low rank adapter based fine-tuning [40, 41, 11, 42].”
LoRA Learns Less and Forgets Less (2024, background): “Studies in the past have hinted at a relationship between the effectiveness of finetuning and model size (Aghajanyan et al., 2020; Hu et al., 2021; Zhuo et al., 2024).”
Parameter-efficient fine-tuning of large-scale pre-trained language models (2023, background): “Instead of resorting to a random subspace 16 , they try to find a common subspace shared by various NLP tasks, which is implemented through decomposing the trained soft prompts of multiple NLP tasks into the same low-dimensional nonlinear subspace, and then learn to adapt the PLM to unseen tasks or…”
VeRA: Vector-based Random Matrix Adaptation (2023, background): “Previous work (Aghajanyan et al., 2021) pointed out the low intrinsic dimensionality of pretrained models’ features.”
Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment (2023, methodology): “We categorize reparameterized fine-tuning methods into two groups: Low-rank Decomposition [11], [42], [43], in which various low-rank decomposition techniques are used to reparameterize the updated matrix, and LoRA derivatives [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55],…”
Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey (2024, background): “Earlier research studies [1] have shown that common pre-trained models exhibit an exceptionally low intrinsic dimensionality.”
Exploring Low-dimensional Intrinsic Task Subspace via Prompt Tuning (2021, background): “…PLMs can be better reparameterized into the same low-dimensional subspace so that the cross-task generalization should be easier, and better pre-training bring lower reparameterization dimensions (Aghajanyan et al., 2021), hence the larger PLM should need less data and tunable parameters.”
Control Prefixes for Parameter-Efficient Text Generation (2021, background): “, 2019); it has also been shown that fine-tuned networks do not deviate substantially from the pretrained one in parameter space (Aghajanyan et al., 2020; Radiya-Dixit and Wang, 2020), implying the existence of parameter efficient alternatives.”