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Rank-Adaptive Time Integration Of Tree Tensor Networks

Publications associées (30)

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Scott William Pesme

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

EPFL2024

Topics in statistical physics of high-dimensional machine learning

Hugo Chao Cui

In the past few years, Machine Learning (ML) techniques have ushered in a paradigm shift, allowing the harnessing of ever more abundant sources of data to automate complex tasks. The technical workhorse behind these important breakthroughs arguably lies in ...

EPFL2024

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Jan Sickmann Hesthaven, Federico Pichi

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 ...

Academic Press Inc Elsevier Science2024

Safe Deep Neural Networks

Kyle Michael Matoba

The capabilities of deep learning systems have advanced much faster than our ability to understand them. Whilst the gains from deep neural networks (DNNs) are significant, they are accompanied by a growing risk and gravity of a bad outcome. This is troubli ...

EPFL2024

Task-driven neural network models predict neural dynamics of proprioception: Experimental data, activations and predictions of neural network models

Axel Bisi, Alberto Silvio Chiappa, Alexander Mathis, Alessandro Marin Vargas

Here we provide the neural data, activation and predictions for the best models and result dataframes of our article "Task-driven neural network models predict neural dynamics of proprioception". It contains the behavioral and neural experimental data (cu ...

EPFL Infoscience2024

Enabling Uncertainty Estimation in Iterative Neural Networks

Pascal Fua, Doruk Oner, Nikita Durasov, Minh Hieu Lê

Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The convergence rate of the ...

Curran Associates2024

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Laura Grigori

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

Siam Publications2024

Random matrix methods for high-dimensional machine learning models

Antoine Philippe Michel Bodin

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

EPFL2024

Reduced Training Data for Laser Ultrasound Signal Interpretation by Neural Networks

Romain Christophe Rémy Fleury, Janez Rus

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 ...

2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Scott William Pesme, Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

Task-driven neural network models predict neural dynamics of proprioception: Neural network model weights

Axel Bisi, Alberto Silvio Chiappa, Alexander Mathis, Alessandro Marin Vargas

Proprioception tells the brain the state of the body based on distributed sensors in the body. However, the principles that govern proprioceptive processing from those distributed sensors are poorly understood. Here, we employ a task-driven neural network ...

Zenodo2024

Infusing structured knowledge priors in neural models for sample-efficient symbolic reasoning

Mattia Atzeni

The ability to reason, plan and solve highly abstract problems is a hallmark of human intelligence. Recent advancements in artificial intelligence, propelled by deep neural networks, have revolutionized disciplines like computer vision and natural language ...

EPFL2024

Coupling a recurrent neural network to SPAD TCSPC systems for real-time fluorescence lifetime imaging

Claudio Bruschini, Edoardo Charbon, Andrei Ardelean, Paul Mos, Yang Lin

Fluorescence lifetime imaging (FLI) has been receiving increased attention in recent years as a powerful diagnostic technique in biological and medical research. However, existing FLI systems often suffer from a tradeoff between processing speed, accuracy, ...

Nature Portfolio2024

Deep learning approach for identification of H II regions during reionization in 21-cm observations - II. Foreground contamination

Michele Bianco, Jean-Paul Richard Kneib, Emma Elizabeth Tolley, Tianyue Chen

The upcoming Square Kilometre Array Observatory will produce images of neutral hydrogen distribution during the epoch of reionization by observing the corresponding 21-cm signal. However, the 21-cm signal will be subject to instrumental limitations such as ...

Oxford Univ Press2024

Measurement of the K+ → π+γγ decay

Alessandro Mapelli, Radoslav Marchevski, Alina Kleimenova

A sample of 3984 candidates of the K+ -> pi(+)gamma gamma decay, with an estimated background of 291 +/- 14 events, was collected by the NA62 experiment at CERN during 2017-2018. In order to describe the observed di-photon mass spectrum, the next-to-leadin ...

Elsevier2024

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Alexandre Caboussat, Marco Picasso, Maude Girardin

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Elsevier Science Sa2024

Sparse autoregressive neural networks for classical spin systems

Giuseppe Carleo, Dian Wu, Indaco Biazzo

Efficient sampling and approximation of Boltzmann distributions involving large sets of binary variables, or spins, are pivotal in diverse scientific fields even beyond physics. Recent advances in generative neural networks have significantly impacted this ...

Iop Publishing Ltd2024

Machine Learning for Modeling Stock Returns

Teng Andrea Xu

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, ...

EPFL2024