Related papers: Learning a Local Symmetry with Neural-Networks

Neural networks are a promising technique for parameterizing sub-grid-scale physics (e.g. moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption.…

Neural networks are a prominent tool for identifying and modeling complex patterns, which are otherwise hard to detect and analyze. While machine learning and neural networks have been finding applications across many areas of science and…

$Anomaly$ $detection$ problems (also called $change$-$point$ $detection$ problems) have been studied in data mining, statistics and computer science over the last several decades in applications such as medical condition monitoring and…

Motivated in part by understanding average case analysis of fundamental algorithms in computer science, and in part by the wide array of network data available over the last decade, a variety of random graph models, with corresponding…

As deep neural networks grow in size, from thousands to millions to billions of weights, the performance of those networks becomes limited by our ability to accurately train them. A common naive question arises: if we have a system with…

We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…

We evaluate the particular performance of different quantum machine learning networks on a graph classification task. Quantum circuits with varying internal symmetry that completely, partially and not at all confer to the symmetry of the…

Recently, machine learning has been applied successfully for identifying phases and phase transitions of the Ising models. The continuous phase transition is characterized by spontaneous symmetry breaking, which can not be detected in…

Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically,…

We have developed a deep neural network that reconstructs the shape of a polygonal domain given the first hundred of its Laplacian eigenvalues. Having an encoder-decoder structure, the network maps input spectra to a latent space and then…

The knowledge of {\it non usual} and sometimes {\it hidden} symmetries of (classical) integrable systems provides a very powerful setting-out of solutions of these models. Primarily, the understanding and possibly the quantisation of…

Modern machine learning systems based on neural networks have shown great success in learning complex data patterns while being able to make good predictions on unseen data points. However, the limited interpretability of these systems…

We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper…

The ability of a feed-forward neural network to learn and classify different states of polymer configurations is systematically explored. Performing numerical experiments, we find that a simple network model can, after adequate training,…

We consider online similarity prediction problems over networked data. We begin by relating this task to the more standard class prediction problem, showing that, given an arbitrary algorithm for class prediction, we can construct an…

Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and…

Symmetry is omnipresent in nature and perceived by the visual system of many species, as it facilitates detecting ecologically important classes of objects in our environment. Symmetry perception requires abstraction of long-range spatial…

The viscosity of lead-containing glasses is of fundamental importance for the manufacturing process, and can be predicted by algorithms such as artificial neural networks. The SciGlass database was used to provide training, validation and…

Neural networks are emerging as a powerful tool for determining the quantum states of interacting many-body fermionic systems. The standard approach trains a neural-network ansatz by minimizing the mean local energy estimated from Monte…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…