Memorization Capacity for Additive Fine-Tuning with Small ReLU Networks

• URL: http://arxiv.org/abs/2408.00359v2
• Date: Mon, 19 Aug 2024 14:15:03 GMT
• Title: Memorization Capacity for Additive Fine-Tuning with Small ReLU Networks
• Authors: Jy-yong Sohn, Dohyun Kwon, Seoyeon An, Kangwook Lee,
• Abstract summary: Fine-Tuning Capacity (FTC) is defined as the maximum number of samples a neural network can fine-tune. We show that $N$ samples can be fine-tuned with $m=Theta(N)$ neurons for 2-layer networks, and with $m=Theta(sqrtN)$ neurons for 3-layer networks, no matter how large $K$ is.
• Score: 16.320374162259117
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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