Memorization Capacity for Additive Fine-Tuning with Small ReLU Networks

Jy-yong Sohn, Dohyun Kwon, Seoyeon An, Kangwook Lee
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:3264-3278, 2024.

Abstract

Fine-tuning large pre-trained models is a common practice in machine learning applications, yet its mathematical analysis remains largely unexplored. In this paper, we study fine-tuning through the lens of memorization capacity. Our new measure, the Fine-Tuning Capacity (FTC), is defined as the maximum number of samples a neural network can fine-tune, or equivalently, as the minimum number of neurons (m) needed to arbitrarily change N labels among K samples considered in the fine-tuning process. In essence, FTC extends the memorization capacity concept to the fine-tuning scenario. We analyze FTC for the additive fine-tuning scenario where the fine-tuned network is defined as the summation of the frozen pre-trained network f and a neural network g (with m neurons) designed for fine-tuning. When g is a ReLU network with either 2 or 3 layers, we obtain tight upper and lower bounds on FTC; we show that N samples can be fine-tuned with m=Θ(N) neurons for 2-layer networks, and with m=Θ(√N) neurons for 3-layer networks, no matter how large K is. Our results recover the known memorization capacity results when N=K as a special case.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-sohn24a, title = {Memorization Capacity for Additive Fine-Tuning with Small ReLU Networks}, author = {Sohn, Jy-yong and Kwon, Dohyun and An, Seoyeon and Lee, Kangwook}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {3264--3278}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/sohn24a/sohn24a.pdf}, url = {https://proceedings.mlr.press/v244/sohn24a.html}, abstract = {Fine-tuning large pre-trained models is a common practice in machine learning applications, yet its mathematical analysis remains largely unexplored. In this paper, we study fine-tuning through the lens of memorization capacity. Our new measure, the Fine-Tuning Capacity (FTC), is defined as the maximum number of samples a neural network can fine-tune, or equivalently, as the minimum number of neurons ($m$) needed to arbitrarily change $N$ labels among $K$ samples considered in the fine-tuning process. In essence, FTC extends the memorization capacity concept to the fine-tuning scenario. We analyze FTC for the additive fine-tuning scenario where the fine-tuned network is defined as the summation of the frozen pre-trained network $f$ and a neural network $g$ (with $m$ neurons) designed for fine-tuning. When $g$ is a ReLU network with either 2 or 3 layers, we obtain tight upper and lower bounds on FTC; we show that $N$ samples can be fine-tuned with $m=\Theta(N)$ neurons for 2-layer networks, and with $m=\Theta(\sqrt{N})$ neurons for 3-layer networks, no matter how large $K$ is. Our results recover the known memorization capacity results when $N = K$ as a special case.} }
Endnote
%0 Conference Paper %T Memorization Capacity for Additive Fine-Tuning with Small ReLU Networks %A Jy-yong Sohn %A Dohyun Kwon %A Seoyeon An %A Kangwook Lee %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-sohn24a %I PMLR %P 3264--3278 %U https://proceedings.mlr.press/v244/sohn24a.html %V 244 %X Fine-tuning large pre-trained models is a common practice in machine learning applications, yet its mathematical analysis remains largely unexplored. In this paper, we study fine-tuning through the lens of memorization capacity. Our new measure, the Fine-Tuning Capacity (FTC), is defined as the maximum number of samples a neural network can fine-tune, or equivalently, as the minimum number of neurons ($m$) needed to arbitrarily change $N$ labels among $K$ samples considered in the fine-tuning process. In essence, FTC extends the memorization capacity concept to the fine-tuning scenario. We analyze FTC for the additive fine-tuning scenario where the fine-tuned network is defined as the summation of the frozen pre-trained network $f$ and a neural network $g$ (with $m$ neurons) designed for fine-tuning. When $g$ is a ReLU network with either 2 or 3 layers, we obtain tight upper and lower bounds on FTC; we show that $N$ samples can be fine-tuned with $m=\Theta(N)$ neurons for 2-layer networks, and with $m=\Theta(\sqrt{N})$ neurons for 3-layer networks, no matter how large $K$ is. Our results recover the known memorization capacity results when $N = K$ as a special case.
APA
Sohn, J., Kwon, D., An, S. & Lee, K.. (2024). Memorization Capacity for Additive Fine-Tuning with Small ReLU Networks. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:3264-3278 Available from https://proceedings.mlr.press/v244/sohn24a.html.

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