Related papers: Sampling the space of solutions of an artificial n…

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…

The uniform sampling of convex regions in high dimension is an important computational issue, from both theoretical and applied point of view. The hit-and-run montecarlo algorithms are the most efficient methods known to perform it and one…

The escalating parameter counts in modern deep learning models pose a fundamental challenge to efficient training and resolution of overfitting. We address this by introducing the \emph{Mapping Networks} which replace the high dimensional…

Today artificial neural networks are applied in various fields - engineering, data analysis, robotics. While they represent a successful tool for a variety of relevant applications, mathematically speaking they are still far from being…

We generalize the Hamiltonian Monte Carlo algorithm with a stack of neural network layers and evaluate its ability to sample from different topologies in a two dimensional lattice gauge theory. We demonstrate that our model is able to…

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most…

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…

This work suggests using sampling theory to analyze the function space represented by neural networks. First, it shows, under the assumption of a finite input domain, which is the common case in training neural networks, that the function…

We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully…

Sparse neural networks are important for achieving better generalization and enhancing computation efficiency. This paper proposes a novel learning approach to obtain sparse fully connected layers in neural networks (NNs) automatically. We…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

The history of deep learning has shown that human-designed problem-specific networks can greatly improve the classification performance of general neural models. In most practical cases, however, choosing the optimal architecture for a…

Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification…

Large and performant neural networks are often overparameterized and can be drastically reduced in size and complexity thanks to pruning. Pruning is a group of methods, which seeks to remove redundant or unnecessary weights or groups of…

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…

We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical…

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…

In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may as well play an important role, resulting in a complex interplay…

The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…