Related papers: A Wigner-Eckart Theorem for Group Equivariant Conv…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

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 these fields. In deep learning, however, these maps are…

Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are…

Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…

It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and…

The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations.…

Mathematically speaking, a transformationally invariant operator, such as a transformationally identical (TI) matrix kernel (i.e., K= T{K}), commutes with the transformation (T{.}) itself when they operate on the first operand matrix. We…

Graph Convolutional Networks (GCNs) have emerged as powerful tools for learning on network structured data. Although empirically successful, GCNs exhibit certain behaviour that has no rigorous explanation -- for instance, the performance of…

Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by long-range interactions among individuals. For example, in bird flocks and fish schools, long-range…

Ideally, 360{\deg} imagery could inherit the deep convolutional neural networks (CNNs) already trained with great success on perspective projection images. However, existing methods to transfer CNNs from perspective to spherical images…

Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…

The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…

We propose a novel class of Gaussian processes (GPs) whose spectra have compact support, meaning that their sample trajectories are almost-surely band limited. As a complement to the growing literature on spectral design of covariance…

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…

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…

The Segal algebra $\mathbf{S}_{0}(G)$ is well defined for arbitrary locally compact Abelian Hausdorff (LCA) groups $G$. It is a Banach space that exhibits a kernel theorem similar to the well-known Schwartz kernel theorem. Specifically, we…

There has been much recent interest in designing neural networks (NNs) with relaxed equivariance, which interpolate between exact equivariance and full flexibility for consistent performance gains. In a separate line of work, structured…

We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis…

Group equivariance is a strong inductive bias useful in a wide range of deep learning tasks. However, constructing efficient equivariant networks for general groups and domains is difficult. Recent work by Finzi et al. (2021) directly…

Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features,…