Related papers: A rank decomposition for the topological classific…

Modern neural networks are usually highly over-parameterized. Behind the wide usage of over-parameterized networks is the belief that, if the data are simple, then the trained network will be automatically equivalent to a simple predictor.…

Network tomography, a classic research problem in the realm of network monitoring, refers to the methodology of inferring unmeasured network attributes using selected end-to-end path measurements. In the research community, network…

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…

The main success stories of deep learning, starting with ImageNet, depend on deep convolutional networks, which on certain tasks perform significantly better than traditional shallow classifiers, such as support vector machines, and also…

Modeling the associations between real world entities from their multivariate cross-sectional profiles can provide cues into the concerted working of these entities as a system. Several techniques have been proposed for deciphering these…

This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of…

The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their…

Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted…

Graph convolution networks (GCNs) have been enormously successful in learning representations over several graph-based machine learning tasks. Specific to learning rich node representations, most of the methods have solely relied on the…

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…

Despite significant advances in graph representation learning, little attention has been paid to the more practical continual learning scenario in which new categories of nodes (e.g., new research areas in citation networks, or new types of…

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…

Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with…

Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…

The subject of deep learning has recently attracted users of machine learning from various disciplines, including: medical diagnosis and bioinformatics, financial market analysis and online advertisement, speech and handwriting recognition,…

The attention that deep learning has garnered from the academic community and industry continues to grow year over year, and it has been said that we are in a new golden age of artificial intelligence research. However, neural networks are…

Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…

We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…