相关论文: Steinmetz Neural Networks for Complex-Valued Data

We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in…

Heterogeneous network data with rich nodal information become increasingly prevalent across multidisciplinary research, yet accurately modeling complex nodal heterogeneity and simultaneously selecting influential nodal attributes remains an…

Deep neural networks (DNNs) have been deployed in myriad machine learning applications. However, advances in their accuracy are often achieved with increasingly complex and deep network architectures. These large, deep models are often…

This paper proposes a new mean-field framework for over-parameterized deep neural networks (DNNs), which can be used to analyze neural network training. In this framework, a DNN is represented by probability measures and functions over its…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

This paper investigates deep neural network (DNN) compression from the perspective of compactly representing and storing trained parameters. We explore the previously overlooked opportunity of cross-layer architecture-agnostic…

Deep neural network (DNN) based approaches hold significant potential for reinforcement learning (RL) and have already shown remarkable gains over state-of-art methods in a number of applications. The effectiveness of DNN methods can be…

Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Recently, innovative adaptations of the Ritz Method incorporating deep learning have been developed, known as the Deep Ritz Method. This approach employs a neural network as the test function for variational problems. However, the neural…

Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack…

Existing graph neural networks may suffer from the "suspended animation problem" when the model architecture goes deep. Meanwhile, for some graph learning scenarios, e.g., nodes with text/image attributes or graphs with long-distance node…

Attenuation bias -- the systematic underestimation of regression coefficients due to measurement errors in input variables -- affects astronomical data-driven models. For linear regression, this problem was solved by treating the true input…

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

We propose a \emph{hybrid} real- and complex-valued \emph{neural network} (HNN) architecture, designed to combine the computational efficiency of real-valued processing with the ability to effectively handle complex-valued data. We…

This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…

Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with…

Convolutional Neural Networks have become state of the art methods for image classification over the last couple of years. By now they perform better than human subjects on many of the image classification datasets. Most of these datasets…

Artificial neural network (ANN) is a very useful tool in solving learning problems. Boosting the performances of ANN can be mainly concluded from two aspects: optimizing the architecture of ANN and normalizing the raw data for ANN. In this…