Related papers: A Computationally Efficient Neural Network Invaria…
Various classes of Graph Neural Networks (GNN) have been proposed and shown to be successful in a wide range of applications with graph structured data. In this paper, we propose a theoretical framework able to compare the expressive power…
Let G be a connected reductive group. In this paper we are studying the invariant theory of symplectic G-modules. Our main result is that the invariant moment map is equidimensional. We deduce that the categorical quotient is a fibration…
While (message-passing) graph neural networks have clear limitations in approximating permutation-equivariant functions over graphs or general relational data, more expressive, higher-order graph neural networks do not scale to large…
We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…
We introduce and investigate, for finite groups $G$, $G$-invariant deep neural network ($G$-DNN) architectures with ReLU activation that are densely connected-- i.e., include all possible skip connections. In contrast to other $G$-invariant…
In complex systems, we often observe complex global behavior emerge from a collection of agents interacting with each other in their environment, with each individual agent acting only on locally available information, without knowing the…
Transformers are a type of neural network that have demonstrated remarkable performance across various domains, particularly in natural language processing tasks. Motivated by this success, research on the theoretical understanding of…
As more deep learning models are being applied in real-world applications, there is a growing need for modeling and learning the representations of neural networks themselves. An efficient representation can be used to predict target…
Many current approaches to machine learning in particle physics use generic architectures that require large numbers of parameters and disregard underlying physics principles, limiting their applicability as scientific modeling tools. In…
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…
Graph-based reasoning over skeleton data has emerged as a promising approach for human action recognition. However, the application of prior graph-based methods, which predominantly employ whole temporal sequences as their input, to the…
We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…
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,…
In this paper, we propose a novel network design mechanism for efficient embedded computing. Inspired by the limited computing patterns, we propose to fix the number of channels in a group convolution, instead of the existing practice that…
Group equivariant convolutional neural networks (G-CNNs) are generalizations of convolutional neural networks (CNNs) which excel in a wide range of technical applications by explicitly encoding symmetries, such as rotations and…
Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…
Let $G$ be a group, $F$ a field, and $A$ a finite-dimensional central simple algebra over $F$ on which $G$ acts by $F$-algebra automorphisms. We study the ideals and subalgebras of $A$ which are preserved by the group action. Let $V$ be the…
In this work we propose a new neural network architecture that efficiently implements and learns general purpose set-equivariant functions. Such a function f maps a set of entities x = {x1, . . . , xn} from one domain to a set of same…
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…
Incorporating group symmetry directly into the learning process has proved to be an effective guideline for model design. By producing features that are guaranteed to transform covariantly to the group actions on the inputs,…