Related papers: A General Method for Proving Networks Universal Ap…

Language models have emerged as a critical area of focus in artificial intelligence, particularly with the introduction of groundbreaking innovations like ChatGPT. Large-scale Transformer networks have quickly become the leading approach…

Neural network based approximate computing is a universal architecture promising to gain tremendous energy-efficiency for many error resilient applications. To guarantee the approximation quality, existing works deploy two neural networks…

While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…

Complex networks are ubiquitous to several Computer Science domains. Centrality measures are an important analysis mechanism to uncover vital elements of complex networks. However, these metrics have high computational costs and…

We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations…

In this study, we explore the inherent trade-off between accuracy and robustness in neural networks, drawing an analogy to the uncertainty principle in quantum mechanics. We propose that neural networks are subject to an uncertainty…

Textual network embeddings aim to learn a low-dimensional representation for every node in the network so that both the structural and textual information from the networks can be well preserved in the representations. Traditionally, the…

Resistor networks have recently been studied as analog computing platforms for machine learning, particularly due to their compatibility with the Equilibrium Propagation training framework. In this work, we explore the computational…

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

Networks are one of the most powerful structures for modeling problems in the real world. Downstream machine learning tasks defined on networks have the potential to solve a variety of problems. With link prediction, for instance, one can…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

Network representation aims to represent the nodes in a network as continuous and compact vectors, and has attracted much attention in recent years due to its ability to capture complex structure relationships inside networks. However,…

Deep neural networks (DNN) have achieved unprecedented performance in computer-vision tasks almost ubiquitously in business, technology, and science. While substantial efforts are made to engineer highly accurate architectures and provide…

Universal Approximation Theorems establish the density of various classes of neural network function approximators in $C(K, \mathbb{R}^m)$, where $K \subset \mathbb{R}^n$ is compact. In this paper, we aim to extend these guarantees by…

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

The great success of deep learning has stimulated avid research activities in verifying the power of depth in theory, a common consensus of which is that deep net are versatile in approximating and learning numerous functions. Such a…

Neural networks have become a popular tool in predictive modelling, more commonly associated with machine learning and artificial intelligence than with statistics. Generalised Additive Models (GAMs) are flexible non-linear statistical…

Complex network topology might get pretty complicated challenging many network analysis objectives, such as community detection for example. This however makes common emergent network phenomena such as scale-free topology or small-world…

A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…