Preventing overfitting in deep learning using differential privacy

Differentially private (DP) training of neural networks is often hindered by the large amount of noise required by gradient-based methods such as DP-SGD, which repeatedly inject high-dimensional noise in parameter space throughout training. In this paper, we propose a new framework for DP learning that avoids iterative optimization in parameter space. Instead of updating the target model using privatized gradients, we employ a hypernetwork trained on public datasets to map a private dataset to the parameters of the target model. Specifically, each example is embedded into a low-dimensional representation, the embeddings are aggregated and perturbed to obtain a DP dataset embedding, and the hypernetwork generates the target model parameters from this noisy embedding. Because privacy noise is injected only once into a low-dimensional dataset representation, our approach can significantly reduce the adverse effect of noise. We theoretically show in a synthetic setting that, under a fixed privacy budget, models produced by our approach achieve higher utility than those trained with DP-SGD. Moreover, we apply our approach to LoRA fine-tuning of diffusion models and show that it achieves lower FID than LoRA models trained with DP-SGD and other public-data-guided methods.

Differentially private machine learning enables model training on sensitive data while ensuring that individual data is unlikely to be recoverable from the parameters of the resulting model. However, existing work often privatizes both training inputs and their labels, and these protections may be conservative when labels are public or can be safely made public. Therefore, in this work we propose a novel private training framework that instead privatizes training inputs while keeping labels public. We consider neural networks with softmax output layers, and thus the mapping from training inputs to the output of the softmax layer is a mapping onto the unit simplex. We randomize softmax outputs during training by applying the Dirichlet mechanism to enforce differential privacy for the training inputs, hence the ``end-to-end'' label. Because training data is reused across multiple training epochs, we use the notion of \Renyi differential privacy to formulate tight bounds on the strength of privacy provided by the Dirichlet mechanism across repeated uses. We show empirically that we attain new state-of-the-art accuracy when training from scratch on CIFAR10, MNIST, MedMNIST, FashionMNIST, and SVHN across all privacy budgets evaluated. Notably, when implementing $(ε, δ)$-differential privacy with $δ=10^{-5}$, we improve the prior state-of-the-art accuracy from $78.37\%$ to $88.17\%$ at $ε=4$ on CIFAR10, and our approach has $82.96\%$ accuracy even for $ε=1$, which significantly outperforms prior work.

Understanding the relationship between generalization and privacy remains a challenge in modern machine learning theory, particularly for deep networks that are trained by variants of differentially private stochastic gradient descent (DP- SGD). In this work we make progress on this persistent open problem. First, we derive explicit upper bounds on the approximate max-information of any algorithm that fulfills $(ε, δ)$-differential privacy or Rényi differential privacy, thereby going beyond the classical results for pure $ε$-differential privacy. Subsequently, we show even stronger guarantees for two common private learning algorithms, output perturbation with the Gaussian mechanism, and streaming DP-SGD, by exploiting the structure of their internal randomization. As an application of our results, we demonstrate how to obtain non-vacuous PAC-Bayes generalization bounds for deep networks, in which the prior distribution is learned by DP-SGD instead of the classical way of choosing it in a data-independent way.