This paper introduces a differential privacy (DP) mechanism for neural tangent kernel (NTK) regression, providing provable guarantees for both privacy and test accuracy. The authors study NTK regression in the context of differential privacy, where NTK is a popular framework for analyzing deep neural networks. They propose a "Gaussian Sampling Mechanism" to add noise to the NTK matrix, ensuring that the resulting matrix remains positive semi-definite (PSD) and maintains good utility. The mechanism is shown to provide $(\epsilon, \delta)$-DP guarantees for NTK regression, with the test accuracy remaining high under a modest privacy budget. Experiments on the CIFAR-10 dataset demonstrate that NTK regression can preserve good accuracy with a small privacy budget, validating the effectiveness of the proposed method. The paper also provides a detailed technical analysis of the sensitivity of the NTK matrix and the privacy-utility trade-off in the proposed mechanism. The results show that the Gaussian Sampling Mechanism can be used to ensure privacy in NTK regression while maintaining high utility, making it a promising approach for privacy-preserving deep learning.This paper introduces a differential privacy (DP) mechanism for neural tangent kernel (NTK) regression, providing provable guarantees for both privacy and test accuracy. The authors study NTK regression in the context of differential privacy, where NTK is a popular framework for analyzing deep neural networks. They propose a "Gaussian Sampling Mechanism" to add noise to the NTK matrix, ensuring that the resulting matrix remains positive semi-definite (PSD) and maintains good utility. The mechanism is shown to provide $(\epsilon, \delta)$-DP guarantees for NTK regression, with the test accuracy remaining high under a modest privacy budget. Experiments on the CIFAR-10 dataset demonstrate that NTK regression can preserve good accuracy with a small privacy budget, validating the effectiveness of the proposed method. The paper also provides a detailed technical analysis of the sensitivity of the NTK matrix and the privacy-utility trade-off in the proposed mechanism. The results show that the Gaussian Sampling Mechanism can be used to ensure privacy in NTK regression while maintaining high utility, making it a promising approach for privacy-preserving deep learning.