Adaptive Laplace Mechanism: Differential Privacy Preservation in Deep Learning

Abstract: In this paper, we focus on developing a novel mechanism to preserve differential privacy in deep neural networks, such that: (1) The privacy budget consumption is totally independent of the number of training steps; (2) It has the ability to adaptively inject noise into features based on the contribution of each to the output; and (3) It could be applied in a variety of different deep neural networks. To achieve this, we figure out a way to perturb affine transformations of neurons, and loss functions used in deep neural networks. In addition, our mechanism intentionally adds "more noise" into features which are "less relevant" to the model output, and vice-versa. Our theoretical analysis further derives the sensitivities and error bounds of our mechanism. Rigorous experiments conducted on MNIST and CIFAR-10 datasets show that our mechanism is highly effective and outperforms existing solutions.

• The paper proposes the Adaptive Laplace Mechanism (AdLM), an innovative method that preserves differential privacy in deep learning by injecting Laplace noise adaptively based on input feature relevance.
• AdLM achieves superior accuracy compared to existing methods like pSGD on datasets such as MNIST and CIFAR-10, maintaining robust performance even with modest privacy budgets.
• This mechanism ensures privacy budget consumption is independent of training steps and is applicable across various deep neural network architectures, offering a scalable solution for sensitive data.
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• Discover the Adaptive Laplace Mechanism, an innovative method preserving differential privacy in deep learning by adaptively injecting noise based on feature relevance.
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• Adaptive Laplace Mechanism for Differential Privacy

Analyzing Differential Privacy Preservation in Deep Learning via the Adaptive Laplace Mechanism

The paper "Adaptive Laplace Mechanism: Differential Privacy Preservation in Deep Learning" presents an innovative method aimed at integrating differential privacy into deep learning processes. Its primary goal is to address the privacy challenges posed by sensitive datasets used in training deep neural networks (DNNs). The authors introduce an Adaptive Laplace Mechanism (AdLM), which reimagines the application of differential privacy by considering the relevance of input features to the model output and adjusting the noise injection accordingly.

Summary of Methodology

The proposed AdLM framework operates under three key objectives:

1. Maintaining independence of privacy budget consumption from the number of training steps;
2. Adapting the injection of noise into features based on each feature's contribution to the model's output;
3. Ensuring applicability across various architectures of deep neural networks.

To achieve this, the authors focus on perturbing affine transformations of neurons and loss functions within the network. This perturbation is conducted by injecting Laplace noise, a common method to achieve differential privacy, into the features that exhibit lesser relevance to the model's output. Conversely, less noise is injected into more relevant features to preserve the utility of the model.

Theoretical Foundations and Implementation

The paper incorporates rigorous theoretical analysis to derive sensitivities and error bounds related to the proposed mechanism. It ensures that the injected noise is distributed adaptively without accumulating the privacy budget during extensive training epochs—a traditional challenge in privacy-preserving models in deep learning.

The implementation of AdLM involves a preprocessing step that computes differentially private relevance of input features by applying Layer-wise Relevance Propagation (LRP). The private relevance helps determine the noise allocation specifically tailored to each feature relative to its importance. Furthermore, the solution comprises injecting noise into the model's affine transformation layers, followed by noise perturbation of a polynomial approximation of the cross-entropy loss function.

Experimental Findings and Implications

Experiments conducted using MNIST and CIFAR-10 datasets demonstrate that AdLM achieves superior accuracy compared to existing privacy-preserving models, such as differentially private stochastic gradient descent (pSGD). Notably, the mechanism achieves robust performance even with modest privacy budget values, suggesting a beneficial reduction in the noise injected during the training process while maintaining the privacy guarantee.

Practical and Theoretical Implications

The adaptivity of the Laplace mechanism proposed in this paper denotes significant progress for differential privacy applications in deep learning. This approach proposes a pathway for deploying deep learning models on sensitive data where privacy concerns are paramount. The mechanism's independence from the number of training epochs could pave the way for more scalable and efficient solutions, especially pertinent for large-scale datasets.

Future Speculations

Looking forward, this paper's contribution could inform future innovations in differential privacy mechanisms wherein noise can be adjusted dynamically based on feature importance—a prospect underscored by advances in interpretability and relevance estimation frameworks like LRP. Moreover, further exploration could explore optimizing privacy budget allocation across various levels of the neural networks, potentially unlocking enhanced utility without compromising privacy.

To summarize, the "Adaptive Laplace Mechanism" paper offers a compelling approach to integrating privacy assurance into the fabric of advanced machine learning models. It opens avenues for further research and development in secure data processing within neural networks, signaling noteworthy potential enhancements in both theoretical algorithms and practical applications.