Related papers: Mathematical Foundation of Interpretable Equivaria…

Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…

This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

This paper explores the characterization of equivariant linear layers for representations of permutations and related groups. Unlike traditional approaches, which address these problems using parameter-sharing, we consider an alternative…

Explanation methods aim to make neural networks more trustworthy and interpretable. In this paper, we demonstrate a property of explanation methods which is disconcerting for both of these purposes. Namely, we show that explanations can be…

Explainable AI is a crucial component for edge services, as it ensures reliable decision making based on complex AI models. Surrogate models are a prominent approach of XAI where human-interpretable models, such as a linear regression…

Phase separation in binary mixtures, governed by the Cahn-Hilliard equation, plays a central role in interfacial dynamics across materials science and soft matter. While numerical solvers are accurate, they are often computationally…

In this work, we propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models, dimension reduction, and generative models, typically employed for performance…

Goal recognition (GR) involves inferring an agent's unobserved goal from a sequence of observations. This is a critical problem in AI with diverse applications. Traditionally, GR has been addressed using 'inference to the best explanation'…

Graph Neural Networks (GNNs) have emerged as the predominant approach for learning over graph-structured data. However, most GNNs operate as black-box models and require post-hoc explanations, which may not suffice in high-stakes scenarios…

\Graph similarity computation is an essential task in many real-world graph-related applications such as retrieving the similar drugs given a query chemical compound or finding the user's potential friends from the social network database.…

Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often…

Deep generative models have recently yielded encouraging results in producing subjectively realistic samples of complex data. Far less attention has been paid to making these generative models interpretable. In many scenarios, ranging from…

Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper,…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable…

With the growing use of deep learning methods, particularly graph neural networks, which encode intricate interconnectedness information, for a variety of real tasks, there is a necessity for explainability in such settings. In this paper,…

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…