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Deep networks learn internal representations whose geometry--how features bend, rotate, and evolve--affects both generalization and robustness. Existing similarity measures such as CKA or SVCCA capture pointwise overlap between activation…

In this paper, an end-to-end nonlinear model reduction methodology is presented based on the convolutional recurrent autoencoder networks. The methodology is developed in the context of the overall data-driven reduced-order model framework…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

In this paper, we propose to exploit the rich hierarchical features of deep convolutional neural networks to improve the accuracy and robustness of visual tracking. Deep neural networks trained on object recognition datasets consist of…

The dynamics in the photosphere is governed by the multi-scale turbulent convection termed as granulation and supergranulation. It is important to derive 3-dimensional velocity vectors to understand the nature of the turbulent convection.…

We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…

In recent years, with the rapid development of computer information technology, the development of artificial intelligence has been accelerating. The traditional geometry recognition technology is relatively backward and the recognition…

The distance-geometric graph representation adopts a unified scheme (distance) for representing the geometry of three-dimensional(3D) graphs. It is invariant to rotation and translation of the graph and it reflects pair-wise node…

We present a deep convolutional neural network for estimating the relative homography between a pair of images. Our feed-forward network has 10 layers, takes two stacked grayscale images as input, and produces an 8 degree of freedom…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

In this paper, we introduce a new framework for unsupervised deep homography estimation. Our contributions are 3 folds. First, unlike previous methods that regress 4 offsets for a homography, we propose a homography flow representation,…

Machine learning is increasingly targeting areas where input data cannot be accurately described by a single vector, but can be modeled instead using the more flexible concept of random vectors, namely probability measures or more simply…

Recent efforts have shown machine learning to be useful for the prediction of nonlinear fluid dynamics. Predictive accuracy is often a central motivation for employing neural networks, but the pattern recognition central to the network…

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

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…

We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of…

State-of-the-art image segmentation algorithms generally consist of at least two successive and distinct computations: a boundary detection process that uses local image information to classify image locations as boundaries between objects,…