Related papers: Understanding Deep Learning using Topological Dyna…

Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by…

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…

We consider a social learning problem, where a network of agents is interested in selecting one among a finite number of hypotheses. We focus on weakly-connected graphs where the network is partitioned into a sending part and a receiving…

Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…

We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subject to nonholonomic constraints. Unlike holonomic constraints,…

Recent years have been marked with the fast-pace diversification and increasing ubiquity of machine learning applications. Yet, a firm theoretical understanding of the surprising efficiency of neural networks to learn from high-dimensional…

Intelligent biological systems are characterized by their embodiment in a complex environment and the intimate interplay between their nervous systems and the nonlinear mechanical properties of their bodies. This coordination, in which the…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

Biological intelligence emerges from substrates that are slow, noisy, and energetically constrained, yet it performs rapid and coherent inference in open-ended environments. Classical computational theories, built around vector-space…

The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and…

We investigate online network topology identification from smooth nodal observations acquired in a streaming fashion. Different from non-adaptive batch solutions, our distinctive goal is to track the (possibly) dynamic adjacency matrix with…

There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;,…

In this paper, we study instances of complex neural networks, i.e. neural netwo rks with complex topologies. We use Self-Organizing Map neural networks whose n eighbourhood relationships are defined by a complex network, to classify handwr…

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

A wavelet-based machine learning method is proposed for predicting the time evolution of homogeneous isotropic turbulence where vortex tubes are preserved. Three-dimensional convolutional neural networks and long short-term memory are…

In a variety of geoscientific applications scientists often need to image properties of the Earth's interior in order to understand the heterogeneity and processes taking place within the Earth. Seismic tomography is one such method which…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…