Related papers: Efficient Representation of Low-Dimensional Manifo…
Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…
We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of…
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…
Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…
Deep networks are now able to achieve human-level performance on a broad spectrum of recognition tasks. Independently, neuromorphic computing has now demonstrated unprecedented energy-efficiency through a new chip architecture based on…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks…
Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…
In the field of pattern recognition research, the method of using deep neural networks based on improved computing hardware recently attracted attention because of their superior accuracy compared to conventional methods. Deep neural…
One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…
Deep convolutional neural networks (DCNNs) have attracted much attention recently, and have shown to be able to recognize thousands of object categories in natural image databases. Their architecture is somewhat similar to that of the human…
Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
Deep artificial neural networks are powerful tools with many possible applications in nanophotonics. Here, we demonstrate how a deep neural network can be used as a fast, general purpose predictor of the full near-field and far-field…
Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…
Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without…
Deep Neural Networks are able to solve many complex tasks with less engineering effort and better performance. However, these networks often use data for training and evaluation without investigating its representation, i.e.~the form of the…