Empirical study of the topology and geometry of deep networks
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In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...
Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...
The performance of machine learning algorithms is conditioned by the availability of training datasets, which is especially true for the field of nondestructive evaluation. Here we propose one reconfigurable specimen instead of numerous reference specimens ...
The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...
Designing novel materials is greatly dependent on understanding the design principles, physical mechanisms, and modeling methods of material microstructures, requiring experienced designers with expertise and several rounds of trial and error. Although rec ...
Throughout history, the pace of knowledge and information sharing has evolved into an unthinkable speed and media. At the end of the XVII century, in Europe, the ideas that would shape the "Age of Enlightenment" were slowly being developed in coffeehouses, ...
Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...
The desire and ability to place AI-enabled applications on the edge has grown significantly in recent years. However, the compute-, area-, and power-constrained nature of edge devices are stressed by the needs of the AI-enabled applications, due to a gener ...
In this thesis we explore the applications of projective geometry, a mathematical theory of the relation between 3D scenes and their 2D images, in modern learning-based computer vision systems. This is an interesting research question which contradicts the ...
Dynamic aperture is an important concept for the study of non-linear beam dynamics in circular accelerators. It describes the extent of the phase-space region where a particle's motion remains bounded over a given number of turns. Understanding the feature ...