Related papers: Continuous approximation by convolutional neural n…
Deep learning models suffer from opaqueness. For Convolutional Neural Networks (CNNs), current research strategies for explaining models focus on the target classes within the associated training dataset. As a result, the understanding of…
We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of $\mathrm{E}(p, q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They cover, for instance,…
Neural networks, especially convolutional neural networks (CNN), are one of the most common tools these days used in computer vision. Most of these networks work with real-valued data using real-valued features. Complex-valued convolutional…
We study the universality of complex-valued neural networks with bounded widths and arbitrary depths. Under mild assumptions, we give a full description of those activation functions $\varrho:\mathbb{C}\to \mathbb{C}$ that have the property…
The approximation power of general feedforward neural networks with piecewise linear activation functions is investigated. First, lower bounds on the size of a network are established in terms of the approximation error and network depth…
Deep convolutional neural networks (CNN) have shown their promise as a universal representation for recognition. However, global CNN activations lack geometric invariance, which limits their robustness for classification and matching of…
In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…
Deep Neural Networks (DNNs) have shown unparalleled achievements in numerous applications, reflecting their proficiency in managing vast data sets. Yet, their static structure limits their adaptability in ever-changing environments. This…
This paper investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…
Although neural networks traditionally are typically used to approximate functions defined over $\mathbb{R}^n$, the successes of graph neural networks, point-cloud neural networks, and manifold deep learning among other methods have…
In recent years, convolutional neural networks (CNNs) have shown great performance in various fields such as image classification, pattern recognition, and multi-media compression. Two of the feature properties, local connectivity and…
Continual learning is the ability to acquire new knowledge without forgetting the previously learned one, assuming no further access to past training data. Neural network approximators trained with gradient descent are known to fail in this…
Deep learning models based on CNNs are predominantly used in image classification tasks. Such approaches, assuming independence of object categories, normally use a CNN as a feature learner and apply a flat classifier on top of it. Object…
Convolutional neural networks (CNNs) are usually built by stacking convolutional operations layer-by-layer. Although CNN has shown strong capability to extract semantics from raw pixels, its capacity to capture spatial relationships of…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…
In the last ten years, Convolutional Neural Networks (CNNs) have formed the basis of deep-learning architectures for most computer vision tasks. However, they are not necessarily optimal. For example, mathematical morphology is known to be…
We prove a negative result for the approximation of functions defined on compact subsets of $\mathbb{R}^d$ (where $d \geq 2$) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a…
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…
We present compositional nearest neighbors (CompNN), a simple approach to visually interpreting distributed representations learned by a convolutional neural network (CNN) for pixel-level tasks (e.g., image synthesis and segmentation). It…