248 citations · 769 across the 15 of their papers we have counts for
14 papers · 1 filter
RoVE: Rotary Value Embeddings Attention for Relative Position-dependent Value Pathways
Alejandro García-Castellanos, Maurice Weiler, Erik J Bekkers
Rotary Position Embeddings (RoPE) make attention scores position-relative but leave the value pathway position-blind: the message sent by a value token is the same regardless of it…
Equivariant non-linear maps for neural networks on homogeneous spaces
Elias Nyholm, Oscar Carlsson, Maurice Weiler +1
This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant -CNNs on homogeneou…
Hyperbolic Convolutional Neural Networks
Andrii Skliar, Maurice Weiler
Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in…
Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
Xuan Zhang, Limei Wang, Jacob Helwig +60
Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating…
Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds
Maurice Weiler, Patrick Forré, Erik Verlinde +1
Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds. A major complication in comparison…
Steerable Partial Differential Operators for Equivariant Neural Networks
Erik Jenner, Maurice Weiler
Recent work in equivariant deep learning bears strong similarities to physics. Fields over a base space are fundamental entities in both subjects, as are equivariant maps between t…
A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels
Leon Lang, Maurice Weiler
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Rece…
Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs
Pim de Haan, Maurice Weiler, Taco Cohen +1
A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs). Such GCNs utilize isotropic kernels and are theref…
Covariance in Physics and Convolutional Neural Networks
Miranda C. N. Cheng, Vassilis Anagiannis, Maurice Weiler +3
In this proceeding we give an overview of the idea of covariance (or equivariance) featured in the recent development of convolutional neural networks (CNNs). We study the similari…
Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Taco S. Cohen, Maurice Weiler, Berkay Kicanaoglu +1
The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent…
A General Theory of Equivariant CNNs on Homogeneous Spaces
Taco Cohen, Mario Geiger, Maurice Weiler
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks…
3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Maurice Weiler, Mario Geiger, Max Welling +2
We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equi…
Intertwiners between Induced Representations (with Applications to the Theory of Equivariant Neural Networks)
Taco S. Cohen, Mario Geiger, Maurice Weiler
Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data suc…
Learning Steerable Filters for Rotation Equivariant CNNs
Maurice Weiler, Fred A. Hamprecht, Martin Storath
In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) i…