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Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…
Convolutional Neural Network (CNN) has gained state-of-the-art results in many pattern recognition and computer vision tasks. However, most of the CNN structures are manually designed by experienced researchers. Therefore, auto- matically…
We develop a deep architecture to learn to find good correspondences for wide-baseline stereo. Given a set of putative sparse matches and the camera intrinsics, we train our network in an end-to-end fashion to label the correspondences as…
The computational prediction of a protein structure from its sequence generally relies on a method to assess the quality of protein models. Most assessment methods rank candidate models using heavily engineered structural features, defined…
Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…
In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…
In previous studies, we introduced a neural network framework based on symmetric differential equations, along with one of its training methods. In this article, we present another training approach for this neural network. This method…
The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular…
Hyperparameter optimization is both a practical issue and an interesting theoretical problem in training of deep architectures. Despite many recent advances the most commonly used methods almost universally involve training multiple and…
Modern pattern recognition tasks use complex algorithms that take advantage of large datasets to make more accurate predictions than traditional algorithms such as decision trees or k-nearest-neighbor better suited to describe simple…
Algorithms based on deep network models are being used for many pattern recognition and decision-making tasks in robotics and AI. Training these models requires a large labeled dataset and considerable computational resources, which are not…
Surgical planning and training based on machine learning requires a large amount of 3D anatomical models reconstructed from medical imaging, which is currently one of the major bottlenecks. Obtaining these data from real patients and during…
In nearest-neighbor classification problems, a set of $d$-dimensional training points are given, each with a known classification, and are used to infer unknown classifications of other points by using the same classification as the nearest…
Understanding transformations under electron beam irradiation requires mapping the structural phases and their evolution in real time. To date, this has mostly been a manual endeavor comprising of difficult frame-by-frame analysis that is…
To gain a deeper understanding of the behavior and learning dynamics of (deep) artificial neural networks, it is valuable to employ mathematical abstractions and models. These tools provide a simplified perspective on network performance…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…
Neural networks are a prominent tool for identifying and modeling complex patterns, which are otherwise hard to detect and analyze. While machine learning and neural networks have been finding applications across many areas of science and…
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…
Neural networks are easier to optimise when they have many more weights than are required for modelling the mapping from inputs to outputs. This suggests a two-stage learning procedure that first learns a large net and then prunes away…