Related papers: On the Completeness of Invariant Geometric Deep Le…

Considering smooth mappings from input vectors to continuous targets, our goal is to characterise subspaces of the input domain, which are invariant under such mappings. Thus, we want to characterise manifolds implicitly defined by level…

Photonic neural networks perform brain-inspired computations using photons instead of electrons that can achieve substantially improved computing performance. However, existing architectures can only handle data with regular structures,…

Graph neural networks (GNNs) are widely used for learning on structured data, yet their ability to distinguish non-isomorphic graphs is fundamentally limited. These limitations are usually attributed to message passing; in this work we show…

Message-passing neural networks (MPNN) have shown extremely high efficiency and accuracy in predicting the physical properties of molecules and crystals, and are expected to become the next-generation material simulation tool after the…

Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop…

Graph Neural Networks (GNNs) have emerged as an efficient alternative to convolutional approaches for vision tasks such as image classification, leveraging patch-based representations instead of raw pixels. These methods construct graphs…

Geometric deep learning has been revolutionizing the molecular modeling field. Despite the state-of-the-art neural network models are approaching ab initio accuracy for molecular property prediction, their applications, such as drug…

Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a…

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to…

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous graph neural networks (GNN) require a large…

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…

$G$-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous $G$-space $\mathcal{M}$. GCNNs are designed to respect the global symmetry in $\mathcal{M}$, thereby facilitating…

Message-passing Graph Neural Networks (GNNs) are often criticized for their limited expressiveness, issues like over-smoothing and over-squashing, and challenges in capturing long-range dependencies. Conversely, Graph Transformers (GTs) are…

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are…

We propose Geometric Neural Parametric Models (GNPM), a learned parametric model that takes into account the local structure of data to learn disentangled shape and pose latent spaces of 4D dynamics, using a geometric-aware architecture on…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…

Graph neural networks (GNNs) learn the representation of graph-structured data, and their expressiveness can be further enhanced by inferring node relations for propagation. Attention-based GNNs infer neighbor importance to manipulate the…

Recent advances in deep convolutional neural networks (CNNs) have motivated researchers to adapt CNNs to directly model points in 3D point clouds. Modeling local structure has been proven to be important for the success of convolutional…