Characterizing the Training Dynamics of Private Fine-tuning with Langevin Diffusion

Shuqi Ke, Charlie Hou, Sewoong Oh, Giulia Fanti

Keywords: differential privacy, convergence, fine-tuning theory, transfer learning theory, langevin diffusion, gradient flow

TL;DR: We provide a quantitative analysis of training and neuron dynamics in private fine-tuning.

Abstract: We show that differentially private full fine-tuning (DP-FFT) can distort pre-trained backbone features based on both theoretical and empirical results. We identify the cause of the distortion as the misalignment between the pre-trained backbone and the randomly initialized linear head. We prove that a sequential fine-tuning strategy can mitigate the feature distortion: first-linear-probing-then-fine-tuning (DP-LP-FFT). A new approximation scheme allows us to derive approximate upper and lower bounds on the training loss of DP-LP and DP-FFT, in a simple but canonical setting of 2-layer neural networks with ReLU activation. Experiments on real-world datasets and architectures are consistent with our theoretical insights. We also derive new upper bounds for 2-layer linear networks without the approximation. Moreover, our theory suggests a trade-off of privacy budget allocation in multi-phase fine-tuning methods like DP-LP-FFT.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 10315