Related papers: Precise Approximation of Convolutional Neural Netw…

We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…

The proliferation of machine learning services in the last few years has raised data privacy concerns. Homomorphic encryption (HE) enables inference using encrypted data but it incurs 100x-10,000x memory and runtime overheads. Secure deep…

Machine learning (ML) algorithms are increasingly important for the success of products and services, especially considering the growing amount and availability of data. This also holds for areas handling sensitive data, e.g. applications…

Modern face recognition systems utilize deep neural networks to extract salient features from a face. These features denote embeddings in latent space and are often stored as templates in a face recognition system. These embeddings are…

In this paper, we address the problem of privacy-preserving federated neural network training with $N$ users. We present Hercules, an efficient and high-precision training framework that can tolerate collusion of up to $N-1$ users. Hercules…

In this work, we consider the approximation of a large class of bounded functions, with minimal regularity assumptions, by ReLU neural networks. We show that the approximation error can be bounded from above by a quantity proportional to…

In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there…

Privacy-preserving neural network (NN) inference can be achieved by utilizing homomorphic encryption (HE), which allows computations to be directly carried out over ciphertexts. Popular HE schemes are built over large polynomial rings. To…

Hybrid Privacy-Preserving Neural Network (HPPNN) implementing linear layers by Homomorphic Encryption (HE) and nonlinear layers by Garbled Circuit (GC) is one of the most promising secure solutions to emerging Machine Learning as a Service…

We study the computation complexity of deep ReLU (Rectified Linear Unit) neural networks for the approximation of functions from the H\"older-Zygmund space of mixed smoothness defined on the $d$-dimensional unit cube when the dimension $d$…

The use of Machine Learning (ML) for data-driven decision-making often relies on access to sensitive datasets, which introduces privacy challenges. Traditional encryption methods protect data at rest or in transit but fail to secure it…

Homomorphic permutation is fundamental to privacy-preserving computations based on batch-encoding homomorphic encryption. It underpins nearly all homomorphic matrix operations and predominantly influences their complexity. Permutation…

Over the decade since deep neural networks became state of the art image classifiers there has been a tendency towards less use of max pooling: the function that takes the largest of nearby pixels in an image. Since max pooling featured…

We study the necessary and sufficient complexity of ReLU neural networks---in terms of depth and number of weights---which is required for approximating classifier functions in $L^2$. As a model class, we consider the set $\mathcal{E}^\beta…

Recently Homomorphic Encryption (HE) is used to implement Privacy-Preserving Neural Networks (PPNNs) that perform inferences directly on encrypted data without decryption. Prior PPNNs adopt mobile network architectures such as SqueezeNet…

We discuss the expressive power of neural networks which use the non-smooth ReLU activation function $\varrho(x) = \max\{0,x\}$ by analyzing the approximation theoretic properties of such networks. The existing results mainly fall into two…

Whereas recovery of the manifold from data is a well-studied topic, approximation rates for functions defined on manifolds are less known. In this work, we study a regression problem with inputs on a $d^*$-dimensional manifold that is…

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…

Two parties wish to collaborate on their datasets. However, before they reveal their datasets to each other, the parties want to have the guarantee that the collaboration would be fruitful. We look at this problem from the point of view of…

We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dimensional PDEs, demonstrating both high accuracy and low…