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The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that need not generalize, while the latter considers classes that…

In studying the expressiveness of neural networks, an important question is whether there are functions which can only be approximated by sufficiently deep networks, assuming their size is bounded. However, for constant depths, existing…

Over the past few years, a tremendous growth of machine learning was brought about by a significant increase in adoption and implementation of cloud-based services. As a result, various solutions have been proposed in which the machine…

Homomorphic Encryption (HE) enables users to securely outsource both the storage and computation of sensitive data to untrusted servers. Not only does HE offer an attractive solution for security in cloud systems, but lattice-based HE…

Recently, Deep Convolutional Neural Networks (DCNNs) including the ResNet-20 architecture have been privately evaluated on encrypted, low-resolution data with the Residue-Number-System Cheon-Kim-Kim-Song (RNS-CKKS) homomorphic encryption…

Neural networks activated by the rectified linear unit (ReLU) play a central role in the recent development of deep learning. The topic of approximating functions from H\"older spaces by these networks is crucial for understanding the…

Large language models (LLMs) power modern AI applications, but processing sensitive data on untrusted servers raises privacy concerns. Homomorphic encryption (HE) enables computation on encrypted data for secure inference. However, neural…

Large language models (LLMs) offer personalized responses based on user interactions, but this use case raises serious privacy concerns. Homomorphic encryption (HE) is a cryptographic protocol supporting arithmetic computations in encrypted…

Outsourcing deep neural networks (DNNs) inference tasks to an untrusted cloud raises data privacy and integrity concerns. While there are many techniques to ensure privacy and integrity for polynomial-based computations, DNNs involve…

In the big data era, cloud-based machine learning as a service (MLaaS) has attracted considerable attention. However, when handling sensitive data, such as financial and medical data, a privacy issue emerges, because the cloud server can…

The widespread adoption of Machine Learning as a Service raises critical privacy and security concerns, particularly about data confidentiality and trust in both cloud providers and the machine learning models. Homomorphic Encryption (HE)…

Federated Learning trains machine learning models on distributed devices by aggregating local model updates instead of local data. However, privacy concerns arise as the aggregated local models on the server may reveal sensitive personal…

Omics data is widely employed in medical research to identify disease mechanisms and contains highly sensitive personal information. Federated Learning (FL) with Differential Privacy (DP) can ensure the protection of omics data privacy…

Recently, many deep networks have introduced hypercomplex and related calculations into their architectures. In regard to convolutional networks for classification, these enhancements have been applied to the convolution operations in the…

We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…

The mod function plays a critical role in numerous data encoding and cryptographic primitives. However, the widely used CKKS homomorphic encryption (HE) scheme supports only arithmetic operations, making it difficult to perform mod…

Machine learning (ML) is widely used today, especially through deep neural networks (DNNs), however, increasing computational load and resource requirements have led to cloud-based solutions. To address this problem, a new generation of…

Privacy-Preserving ML (PPML) based on Homomorphic Encryption (HE) is a promising foundational privacy technology. Making it more practical requires lowering its computational cost, especially, in handling modern large deep neural networks.…

This paper focuses on approximation and learning performance analysis for deep convolutional neural networks with zero-padding and max-pooling. We prove that, to approximate $r$-smooth function, the approximation rates of deep convolutional…

Outsourced computation for neural networks allows users access to state of the art models without needing to invest in specialized hardware and know-how. The problem is that the users lose control over potentially privacy sensitive data.…