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Deep neural networks (DNNs) are so over-parametrized that recent research has found them to already contain a subnetwork with high accuracy at their randomly initialized state. Finding these subnetworks is a viable alternative training…

The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…

Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…

Artificial neural networks have become important to improve the search for admissible string compactifications and characterize them. In this paper we construct the heterotic orbiencoder, a general deep autoencoder to study heterotic…

Image representations, from SIFT and Bag of Visual Words to Convolutional Neural Networks (CNNs), are a crucial component of almost any image understanding system. Nevertheless, our understanding of them remains limited. In this paper we…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

In image classification task, feature extraction is always a big issue. Intra-class variability increases the difficulty in designing the extractors. Furthermore, hand-crafted feature extractor cannot simply adapt new situation. Recently,…

Single-shot wide-angle diffraction imaging is a widely used method to investigate the structure of non-crystallizing objects such as nanoclusters, large proteins or even viruses. Its main advantage is that information about the…

We introduce a probability distribution, combined with an efficient sampling algorithm, for weights and biases of fully-connected neural networks. In a supervised learning context, no iterative optimization or gradient computations of…

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…

Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and…

We present a new latent model of natural images that can be learned on large-scale datasets. The learning process provides a latent embedding for every image in the training dataset, as well as a deep convolutional network that maps the…

We investigate a human-machine collaborative drawing environment in which an autonomous agent sketches images while optionally allowing a user to directly influence the agent's trajectory. We combine Monte Carlo Tree Search with image…

It has been recently shown that neural networks can recover the geometric structure of a face from a single given image. A common denominator of most existing face geometry reconstruction methods is the restriction of the solution space to…

In many branches of earth sciences, the problem of rock study on the micro-level arises. However, a significant number of representative samples is not always feasible. Thus the problem of the generation of samples with similar properties…

Deep learning applied to the reconstruction of 3D shapes has seen growing interest. A popular approach to 3D reconstruction and generation in recent years has been the CNN encoder-decoder model usually applied in voxel space. However, this…

A key goal of computer vision is to recover the underlying 3D structure from 2D observations of the world. In this paper we learn strong deep generative models of 3D structures, and recover these structures from 3D and 2D images via…

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…