Related papers: Approximately Equivariant Networks for Imperfectly…

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…

Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong induction bias for the…

We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a…

Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than…

Equivariant neural networks exploit underlying task symmetries to improve generalization, but strict equivariance constraints can induce more complex optimization dynamics that can hinder learning. Prior work addresses these limitations by…

Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries. By construction ENNs cannot produce lower symmetry outputs given a higher symmetry input. However, symmetry…

This paper investigates the super-resolution (SR) of velocity fields in two-dimensional fluids from the viewpoint of rotational equivariance. SR refers to techniques that estimate high-resolution images from those in low resolution and has…

For many years, it has been shown how much exploiting equivariances can be beneficial when solving image analysis tasks. For example, the superiority of convolutional neural networks (CNNs) compared to dense networks mainly comes from an…

Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently this idea has been…

As supervised learning still dominates most AI applications, test-time performance is often unexpected. Specifically, a shift of the input covariates, caused by typical nuisances like background-noise, illumination variations or…

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…

Many algorithms and observed phenomena in deep learning appear to be affected by parameter symmetries -- transformations of neural network parameters that do not change the underlying neural network function. These include linear mode…

Convolutional neural networks (CNNs) have recently been applied to predict or model fluid dynamics. However, mechanisms of CNNs for learning fluid dynamics are still not well understood, while such understanding is highly necessary to…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge…

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…

Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…

Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We…

In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the…

This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…