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Incorporating spectral information to enhance Graph Neural Networks (GNNs) has shown promising results but raises a fundamental challenge due to the inherent ambiguity of eigenvectors. Various architectures have been proposed to address…
Neural Persistence is a prominent measure for quantifying neural network complexity, proposed in the emerging field of topological data analysis in deep learning. In this work, however, we find both theoretically and empirically that the…
This is a master's thesis concerning the theoretical ideas of geometric deep learning. Geometric deep learning aims to provide a structured characterization of neural network architectures, specifically focused on the ideas of invariance…
Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant…
The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…
With the substantial performance of neural networks in sensitive fields increases the need for interpretable deep learning models. Major challenge is to uncover the multiscale and distributed representation hidden inside the basket mappings…
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…
Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…
Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…
Place recognition is one of the most challenging problems in computer vision, and has become a key part in mobile robotics and autonomous driving applications for performing loop closure in visual SLAM systems. Moreover, the difficulty of…
Convolutional neural networks are witnessing wide adoption in computer vision systems with numerous applications across a range of visual recognition tasks. Much of this progress is fueled through advances in convolutional neural network…
Utilizing physics-informed neural networks (PINN) to solve partial differential equations (PDEs) becomes a hot issue and also shows its great powers, but still suffers from the dilemmas of limited predicted accuracy in the sampling domain…
This paper investigates the feasibility of using Graph Neural Networks (GNNs) for classical motion planning problems. We propose guiding both continuous and discrete planning algorithms using GNNs' ability to robustly encode the topology of…
Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…
Training deep networks that generalize to a wide range of variations in test data is essential to building accurate and robust image classifiers. One standard strategy is to apply data augmentation to synthetically enlarge the training set.…
Graph Neural Networks (GNNs) have displayed considerable promise in graph representation learning across various applications. The core learning process requires the initialization of model weight matrices within each GNN layer, which is…
Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…
In this work, we present and study Continuous Generative Neural Networks (CGNNs), namely, generative models in the continuous setting: the output of a CGNN belongs to an infinite-dimensional function space. The architecture is inspired by…
Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…
Generalizing a pretrained model to unseen datasets without retraining is an essential step toward a foundation model. However, achieving such cross-dataset, fully inductive inference is difficult in graph-structured data where feature…