相关论文: Universal approximation property of invertible neu…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

Hypercomplex neural networks are gaining increasing interest in the deep learning community. The attention directed towards hypercomplex models originates from several aspects, spanning from purely theoretical and mathematical…

Inverse problems are extensively studied in applied mathematics, with applications ranging from acoustic tomography for medical diagnosis to geophysical exploration. Physics informed neural networks (PINNs) have emerged as a powerful tool…

Task-based modeling with recurrent neural networks (RNNs) has emerged as a popular way to infer the computational function of different brain regions. These models are quantitatively assessed by comparing the low-dimensional neural…

The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…

Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…

Universal approximation theorem suggests that a shallow neural network can approximate any function. The input to neurons at each layer is a weighted sum of previous layer neurons and then an activation is applied. These activation…

Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation…

Universality of neural networks describes the ability to approximate arbitrary function, and is a key ingredient to keep the method effective. The established models for universal quantum neural networks(QNN), however, require the…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

Modern discriminative predictors have been shown to match natural intelligences in specific perceptual tasks in image classification, object and part detection, boundary extraction, etc. However, a major advantage that natural intelligences…

Deep learning as represented by the artificial deep neural networks (DNNs) has achieved great success in many important areas that deal with text, images, videos, graphs, and so on. However, the black-box nature of DNNs has become one of…

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

We present a constructive universal approximation theorem for learning machines equipped with joint-group-equivariant feature maps, called the joint-equivariant machines, based on the group representation theory. ``Constructive'' here…

We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective. We prove that deep residual fully convolutional networks and their continuous-layer…

Input-Convex Neural Networks (ICNNs) are networks that guarantee convexity in their input-output mapping. These networks have been successfully applied for energy-based modelling, optimal transport problems and learning invariances. The…

Neural network representations are often analyzed as vectors in a fixed Euclidean space. However, their coordinates are not uniquely defined. If a hidden representation is transformed by an invertible linear map, the network function can be…