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We introduce Active Predictive Coding Networks (APCNs), a new class of neural networks that solve a major problem posed by Hinton and others in the fields of artificial intelligence and brain modeling: how can neural networks learn…

Deep neural networks have become ubiquitous for applications related to visual recognition and language understanding tasks. However, it is often prohibitive to use typical neural networks on devices like mobile phones or smart watches…

Capsule Networks (CapsNets) are brand-new architectures that have shown ground-breaking results in certain areas of Computer Vision (CV). In 2017, Hinton and his team introduced CapsNets with routing-by-agreement in "Sabour et al" and in a…

Designing effective models for learning time series representations is foundational for time series analysis. Many previous works have explored time series representation modeling approaches and have made progress in this area. Despite…

Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…

In order to solve the robustness and generality problems of the image fusion task,inspired by the human brain cognitive mechanism, we propose a robust and general image fusion method with autonomous evolution ability, and is therefore…

The success of Neural networks in providing miraculous results when applied to a wide variety of tasks is astonishing. Insight in the working can be obtained by studying the universal approximation property of neural networks. It is proved…

While deep learning has achieved great success in computer vision and many other fields, currently it does not work very well on patient genomic data with the "big p, small N" problem (i.e., a relatively small number of samples with…

This paper presents a novel adaptively connected neural network (ACNet) to improve the traditional convolutional neural networks (CNNs) {in} two aspects. First, ACNet employs a flexible way to switch global and local inference in processing…

The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…

Optical neural networks promise ultrafast, low-energy information processing by performing computation directly with photons. Current implementations, however, are largely restricted to steady-state operation and rely on high-latency…

\citet{farrell2021deep} establish non-asymptotic high-probability bounds for general deep feedforward neural network (with rectified linear unit activation function) estimators, with \citet[Theorem 1]{farrell2021deep} achieving a suboptimal…

Convolutional neural networks (CNNs) are the cutting edge model for supervised machine learning in computer vision. In recent years CNNs have outperformed traditional approaches in many computer vision tasks such as object detection, image…

At present, the great achievements of convolutional neural network(CNN) in feature and metric learning have attracted many researchers. However, the vast majority of deep network architectures have been used to represent based on real…

The inverse statistical problem of finding direct interactions in complex networks is difficult. In the natural sciences, well-controlled perturbation experiments are widely used to probe the structure of complex networks. However, our…

The classical universal approximation (UA) theorem for neural networks establishes mild conditions under which a feedforward neural network can approximate a continuous function $f$ with arbitrary accuracy. A recent result shows that neural…

Most stochastic gradient descent algorithms can optimize neural networks that are sub-differentiable in their parameters; however, this implies that the neural network's activation function must exhibit a degree of continuity which limits…

Accurate medical image segmentation is essential for diagnosis and treatment planning of diseases. Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance for automatic medical image segmentation. However, they are…

Classical results in neural network approximation theory show how arbitrary continuous functions can be approximated by networks with a single hidden layer, under mild assumptions on the activation function. However, the classical theory…

We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…