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Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations,…

Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural networks to a wide…

Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…

Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

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 $G$-CNNs on homogeneous spaces characterized the representation theory of such…

Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

Equivariance w.r.t. geometric transformations in neural networks improves data efficiency, parameter efficiency and robustness to out-of-domain perspective shifts. When equivariance is not designed into a neural network, the network can…

The task of fully inductive link prediction in knowledge graphs has gained significant attention, with various graph neural networks being proposed to address it. This task presents greater challenges than traditional inductive link…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…

Latent representations are used extensively for downstream tasks, such as visualization, interpolation or feature extraction of deep learning models. Invariant and equivariant neural networks are powerful and well-established models for…

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…

Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…

Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers.…