Related papers: Revisiting Transformation Invariant Geometric Deep…
Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…
In this contribution, we show how to incorporate prior knowledge to a deep neural network architecture in a principled manner. We enforce feature space invariances using a novel layer based on invariant integration. This allows us to…
Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…
Convolutional Neural Networks(CNN) are inherently equivariant under translations, however, they do not have an equivalent embedded mechanism to handle other transformations such as rotations and change in scale. Several approaches exist…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
Graph Neural Networks (GNNs) have demonstrated remarkable success in various applications, yet they often struggle to capture long-range dependencies (LRD) effectively. This paper introduces GraphMinNet, a novel GNN architecture that…
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture…
Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…
This work examines the deep disconnect between existing theoretical analyses of gradient-based algorithms and the practice of training deep neural networks. Specifically, we provide numerical evidence that in large-scale neural network…
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,…
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
Deep-learning has achieved good performance and shown great potential for solving forward and inverse problems. In this work, two categories of innovative deep-learning based inverse modeling methods are proposed and compared. The first…
Point cloud analysis is an area of increasing interest due to the development of 3D sensors that are able to rapidly measure the depth of scenes accurately. Unfortunately, applying deep learning techniques to perform point cloud analysis is…
Deep neural networks (DNN) have achieved great success in image restoration. However, most DNN methods are designed as a black box, lacking transparency and interpretability. Although some methods are proposed to combine traditional…
Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other…
Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…
Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model…
Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data…
Most current deep learning models equivariant to $O(n)$ or $SO(n)$ either consider mostly scalar information such as distances and angles or have a very high computational complexity. In this work, we test a few novel message passing graph…