Related papers: Precise Approximation of Convolutional Neural Netw…

In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime…

A key challenge in scientific machine learning is solving partial differential equations (PDEs) on complex domains, where the curved geometry complicates the approximation of functions and their derivatives required by differential…

The widespread adoption of cloud-based solutions introduces privacy and security concerns. Techniques such as homomorphic encryption (HE) mitigate this problem by allowing computation over encrypted data without the need for decryption.…

Large language models(LLMs) are currently at the forefront of the machine learning field, which show a broad application prospect but at the same time expose some risks of privacy leakage. We combined Fully Homomorphic Encryption(FHE) and…

In this letter, we propose HV-Net, a new method for hypervolume approximation in evolutionary multi-objective optimization. The basic idea of HV-Net is to use DeepSets, a deep neural network with permutation invariant property, to…

This paper investigates the relationship between the universal approximation property of deep neural networks and topological characteristics of datasets. Our primary contribution is to introduce data topology-dependent upper bounds on the…

Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, such…

With the rapid surge in the prevalence of Large Language Models (LLMs), individuals are increasingly turning to conversational AI for initial insights across various domains, including health-related inquiries such as disease diagnosis.…

Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part due to simulations…

Machine learning on encrypted data can address the concerns related to privacy and legality of sharing sensitive data with untrustworthy service providers. Fully Homomorphic Encryption (FHE) is a promising technique to enable machine…

In this technical report, we explore the use of homomorphic encryption (HE) in the context of training and predicting with deep learning (DL) models to deliver strict \textit{Privacy by Design} services, and to enforce a zero-trust model of…

Among the several paradigms of artificial intelligence (AI) or machine learning (ML), a remarkably successful paradigm is deep learning. Deep learning's phenomenal success has been hoped to be interpreted via fundamental research on the…

Fully Homomorphic Encryption (FHE) has the potential to substantially improve privacy and security by enabling computation directly on encrypted data. This is especially true with deep learning, as today, many popular user services are…

We explore the phase diagram of approximation rates for deep neural networks and prove several new theoretical results. In particular, we generalize the existing result on the existence of deep discontinuous phase in ReLU networks to…

We consider approximations of general continuous functions on finite-dimensional cubes by general deep ReLU neural networks and study the approximation rates with respect to the modulus of continuity of the function and the total number of…

Deep hashing techniques have emerged as the predominant approach for efficient image retrieval. Traditionally, these methods utilize pre-trained convolutional neural networks (CNNs) such as AlexNet and VGG-16 as feature extractors. However,…

Federated fine-tuning is critical for improving the performance of large language models (LLMs) in handling domain-specific tasks while keeping training data decentralized and private. However, prior work has shown that clients' private…

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

Heterogeneous data is endemic due to the use of diverse models and settings of devices by hospitals in the field of medical imaging. However, there are few open-source frameworks for federated heterogeneous medical image analysis with…

We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes in $L^2(\mathbb R^d)$. In other words, we establish a…