Related papers: A Practical Method for Constructing Equivariant Mu…

We present a simple non-generative approach to deep representation learning that seeks equivariant deep embedding through simple objectives. In contrast to existing equivariant networks, our transformation coding approach does not constrain…

In this work we obtain the general form of polynomial mappings that commute with a linear action of a relative symmetry group. The aim is to give results for relative equivariant polynomials that correspond to the results for relative…

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared…

We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed data -- called a complex of groups -- amounts to a functor from (the…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…

Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing to classifying implicit neural representation. Previous NFN…

Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heuristic, and the…

Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite…

Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural…

Downsampling layers are crucial building blocks in CNN architectures, which help to increase the receptive field for learning high-level features and reduce the amount of memory/computation in the model. In this work, we study the…

Many data symmetries can be described in terms of group equivariance and the most common way of encoding group equivariances in neural networks is by building linear layers that are group equivariant. In this work we investigate whether…

The difficult problem of relating the static structure of glassy liquids and their dynamics is a good target for Machine Learning, an approach which excels at finding complex patterns hidden in data. Indeed, this approach is currently a hot…

Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve…

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising…

The simplicity and effectiveness of the UNet architecture makes it ubiquitous in image restoration, image segmentation, and diffusion models. They are often assumed to be equivariant to translations, yet they traditionally consist of layers…

The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the…

Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…

Equivariance encodes known symmetries into neural networks, often enhancing generalization. However, equivariant networks cannot break symmetries: the output of an equivariant network must, by definition, have at least the same…