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This paper presents a framework of successive functional gradient optimization for training nonconvex models such as neural networks, where training is driven by mirror descent in a function space. We provide a theoretical analysis and…

Machine Learning · Computer Science 2020-07-01 Rie Johnson , Tong Zhang

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and…

Machine Learning · Computer Science 2023-02-28 Nathaniel Trask , Ravi G. Patel , Ben J. Gross , Paul J. Atzberger

Graph Drawing techniques have been developed in the last few years with the purpose of producing aesthetically pleasing node-link layouts. Recently, the employment of differentiable loss functions has paved the road to the massive usage of…

Machine Learning · Computer Science 2022-07-04 Matteo Tiezzi , Gabriele Ciravegna , Marco Gori

Neural networks are trained by choosing an architecture and training the parameters. The choice of architecture is often by trial and error or with Neural Architecture Search (NAS) methods. While NAS provides some automation, it often…

Machine Learning · Computer Science 2024-10-14 Zitong Huang , Mansooreh Montazerin , Ajitesh Srivastava

Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…

Computer Vision and Pattern Recognition · Computer Science 2013-06-07 Eckhard Hitzer

This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying…

Graphics · Computer Science 2020-05-06 Hsueh-Ti Derek Liu , Vladimir G. Kim , Siddhartha Chaudhuri , Noam Aigerman , Alec Jacobson

Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heuristic, and the…

Machine Learning · Computer Science 2021-06-18 Jiahao Su , Wonmin Byeon , Furong Huang

Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and therefore, end-to-end training is…

Computer Vision and Pattern Recognition · Computer Science 2022-02-01 Christoph Angermann , Markus Haltmeier

We propose a new training method for a feedforward neural network having the activation functions with the geometric contraction property. The method consists of constructing a new functional that is less nonlinear in comparison with the…

Neural and Evolutionary Computing · Computer Science 2018-08-14 Petre Birtea , Cosmin Cernazanu-Glavan , Alexandru Sisu

We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes…

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…

Machine Learning · Computer Science 2016-06-09 Mathias Niepert , Mohamed Ahmed , Konstantin Kutzkov

Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…

Optimization and Control · Mathematics 2026-01-14 Jona-Maria Diederen , Holger Rauhut , Ulrich Terstiege

Tracking a horizon in seismic images or 3D volumes is an integral part of seismic interpretation. The last few decades saw progress in using neural networks for this task, starting from shallow networks for 1D traces, to deeper…

Geophysics · Physics 2020-03-20 Bas Peters , Eldad Haber

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…

Machine Learning · Computer Science 2020-03-27 Muhammet Balcilar , Guillaume Renton , Pierre Heroux , Benoit Gauzere , Sebastien Adam , Paul Honeine

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…

Machine Learning · Computer Science 2022-11-29 Richard D. Lange , Devin Kwok , Jordan Matelsky , Xinyue Wang , David S. Rolnick , Konrad P. Kording

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…

Machine Learning · Computer Science 2017-04-25 Federico Monti , Michael M. Bronstein , Xavier Bresson

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative…

Machine Learning · Computer Science 2025-07-21 Arturs Berzins , Andreas Radler , Eric Volkmann , Sebastian Sanokowski , Sepp Hochreiter , Johannes Brandstetter

Standard convolutional neural networks assume a grid structured input is available and exploit discrete convolutions as their fundamental building blocks. This limits their applicability to many real-world applications. In this paper we…

Computer Vision and Pattern Recognition · Computer Science 2021-01-19 Shenlong Wang , Simon Suo , Wei-Chiu Ma , Andrei Pokrovsky , Raquel Urtasun

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…

Machine Learning · Computer Science 2020-07-10 Amos Gropp , Lior Yariv , Niv Haim , Matan Atzmon , Yaron Lipman

This is a master's thesis concerning the theoretical ideas of geometric deep learning. Geometric deep learning aims to provide a structured characterization of neural network architectures, specifically focused on the ideas of invariance…

Machine Learning · Computer Science 2023-01-24 Gerrit Nolte