Lattice gauge equivariant convolutional neural networks

• URL: http://arxiv.org/abs/2012.12901v1
• Date: Wed, 23 Dec 2020 19:00:01 GMT
• Title: Lattice gauge equivariant convolutional neural networks
• Authors: Matteo Favoni, Andreas Ipp, David I. M\"uller, Daniel Schuh
• Abstract summary: We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications. We show that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.

Related papers

• Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
  We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs) Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators. Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
  arXiv  Detail & Related papers  (2024-05-22T17:23:15Z)
• Graph Neural Networks for Learning Equivariant Representations of Neural Networks [55.04145324152541]
  We propose to represent neural networks as computational graphs of parameters. Our approach enables a single model to encode neural computational graphs with diverse architectures. We showcase the effectiveness of our method on a wide range of tasks, including classification and editing of implicit neural representations.
  arXiv  Detail & Related papers  (2024-03-18T18:01:01Z)
• Geometrical aspects of lattice gauge equivariant convolutional neural networks [0.0]
  Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories.
  arXiv  Detail & Related papers  (2023-03-20T20:49:08Z)
• Permutation Equivariant Neural Functionals [92.0667671999604]
  This work studies the design of neural networks that can process the weights or gradients of other neural networks. We focus on the permutation symmetries that arise in the weights of deep feedforward networks because hidden layer neurons have no inherent order. In our experiments, we find that permutation equivariant neural functionals are effective on a diverse set of tasks.
  arXiv  Detail & Related papers  (2023-02-27T18:52:38Z)
• Applications of Lattice Gauge Equivariant Neural Networks [0.0]
  Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs) L-CNNs can generalize better to differently sized lattices than traditional neural networks. We present our progress on possible applications of L-CNNs to Wilson flow or continuous normalizing flow.
  arXiv  Detail & Related papers  (2022-12-01T19:32:42Z)
• Interrelation of equivariant Gaussian processes and convolutional neural networks [77.34726150561087]
  Currently there exists rather promising new trend in machine leaning (ML) based on the relationship between neural networks (NN) and Gaussian processes (GP) In this work we establish a relationship between the many-channel limit for CNNs equivariant with respect to two-dimensional Euclidean group with vector-valued neuron activations and the corresponding independently introduced equivariant Gaussian processes (GP)
  arXiv  Detail & Related papers  (2022-09-17T17:02:35Z)
• On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Bias [50.84569563188485]
  We show that gradient flow converges in direction when labels are determined by the sign of a target network with $r$ neurons. Our result may already hold for mild over- parameterization, where the width is $tildemathcalO(r)$ and independent of the sample size.
  arXiv  Detail & Related papers  (2022-05-18T16:57:10Z)
• Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need? [80.86819657126041]
  We show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks.
  arXiv  Detail & Related papers  (2021-12-23T03:52:33Z)
• Preserving gauge invariance in neural networks [0.0]
  lattice gauge equivariant convolutional neural networks (L-CNNs) We show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice.
  arXiv  Detail & Related papers  (2021-12-21T14:08:12Z)
• Lattice gauge symmetry in neural networks [0.0]
  We review a novel neural network architecture called lattice gauge equivariant convolutional neural networks (L-CNNs) We discuss the concept of gauge equivariance which we use to explicitly construct a gauge equivariant convolutional layer and a bilinear layer. The performance of L-CNNs and non-equivariant CNNs is compared using seemingly simple non-linear regression tasks.
  arXiv  Detail & Related papers  (2021-11-08T11:20:11Z)
• Implicit Bias of Linear Equivariant Networks [2.580765958706854]
  Group equivariant convolutional neural networks (G-CNNs) are generalizations of convolutional neural networks (CNNs) We show that $L$-layer full-width linear G-CNNs trained via gradient descent converge to solutions with low-rank Fourier matrix coefficients.
  arXiv  Detail & Related papers  (2021-10-12T15:34:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.