Related papers: Frame Averaging for Invariant and Equivariant Netw…

This work seeks to improve the generalization and robustness of existing neural networks for 3D point clouds by inducing group equivariance under general group transformations. The main challenge when designing equivariant models for point…

Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…

Understanding feature learning is an important open question in establishing a mathematical foundation for deep neural networks. The Neural Feature Ansatz (NFA) states that after training, the Gram matrix of the first-layer weights of a…

The ability to generalize compositionally is key to understanding the potentially infinite number of sentences that can be constructed in a human language from only a finite number of words. Investigating whether NLP models possess this…

Recently, machine learning (ML) has been used to address the computational cost that has been limiting ab initio molecular dynamics (AIMD). Here, we present GNNFF, a graph neural network framework to directly predict atomic forces from…

We investigate the generalization error of group-invariant neural networks within the Barron framework. Our analysis shows that incorporating group-invariant structures introduces a group-dependent factor $\delta_{G,\Gamma,\sigma} \le 1$…

Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards…

Invariant learning demonstrates substantial potential for enhancing the generalization of graph neural networks (GNNs) with out-of-distribution (OOD) data. It aims to recognize stable features in graph data for classification, based on the…

Conditional Neural Fields (CNFs) are increasingly being leveraged as continuous signal representations, by associating each data-sample with a latent variable that conditions a shared backbone Neural Field (NeF) to reconstruct the sample.…

In this study, we introduce a method for learning group (known or unknown) equivariant functions by learning the associated quadratic form $x^T A x$ corresponding to the group from the data. Certain groups, known as orthogonal groups,…

Bayesian inference offers a robust framework for updating prior beliefs based on new data using Bayes' theorem, but exact inference is often computationally infeasible, necessitating approximate methods. Though widely used, these methods…

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…

We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element…

Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to…

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…

Graph matching, typically formulated as a Quadratic Assignment Problem (QAP), seeks to establish node correspondences between two graphs. To address the NP-hardness of QAP, some existing methods adopt projection-based relaxations that embed…

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…

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

In this draft paper, we introduce a novel architecture for graph networks which is equivariant to the Euclidean group in $n$-dimensions. The model is designed to work with graph networks in their general form and can be shown to include…