Related papers: Deep Hamiltonian networks based on symplectic inte…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
Neural network training and validation rely on the availability of large high-quality datasets. However, in many cases only incomplete datasets are available, particularly in health care applications, where each patient typically undergoes…
Convolutional neural networks often dominate fully-connected counterparts in generalization performance, especially on image classification tasks. This is often explained in terms of 'better inductive bias'. However, this has not been made…
We introduce Hyper Input Convex Neural Networks (HyCNNs), a novel neural network architecture designed for learning convex functions. HyCNNs combine the principles of Maxout networks with input convex neural networks (ICNNs) to create a…
We present the Hue-Net - a novel Deep Learning framework for Intensity-based Image-to-Image Translation. The key idea is a new technique termed network augmentation which allows a differentiable construction of intensity histograms from…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…
The problem of attributing a deep network's prediction to its \emph{input/base} features is well-studied. We introduce the notion of \emph{conductance} to extend the notion of attribution to the understanding the importance of \emph{hidden}…
Computer vision researchers have been expecting that neural networks have spatial transformation ability to eliminate the interference caused by geometric distortion for a long time. Emergence of spatial transformer network makes dream come…
Using machine learning, we explore the utility of various deep neural networks (NN) when applied to high harmonic generation (HHG) scenarios. First, we train the NNs to predict the time-dependent dipole and spectra of HHG emission from…
We investigate the geometric properties of the functions learned by trained ConvNets in the preactivation space of their convolutional layers, by performing an empirical study of hyperplane arrangements induced by a convolutional layer. We…
A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…
In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…
Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…
In the field of medical CT image processing, convolutional neural networks (CNNs) have been the dominant technique.Encoder-decoder CNNs utilise locality for efficiency, but they cannot simulate distant pixel interactions properly.Recent…
This study delves into the intricate dynamics of trained deep neural networks and their relationships with network parameters. Trained networks predominantly continue training in a single direction, known as the drift mode. This drift mode…
Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral methods based on their…
This paper presents HGEN that pioneers ensemble learning for heterogeneous graphs. We argue that the heterogeneity in node types, nodal features, and local neighborhood topology poses significant challenges for ensemble learning,…
In i-theory a typical layer of a hierarchical architecture consists of HW modules pooling the dot products of the inputs to the layer with the transformations of a few templates under a group. Such layers include as special cases the…