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The ability to compute similarity scores between graphs based on metrics such as Graph Edit Distance (GED) is important in many real-world applications. Computing exact GED values is typically an NP-hard problem and traditional algorithms…

Bayesian Neural Networks(BNNs) with high-dimensional parameters pose a challenge for posterior inference due to the multi-modality of the posterior distributions. Stochastic Gradient MCMC(SGMCMC) with cyclical learning rate scheduling is a…

Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…

With the maturation of quantum computing technology, research has gradually shifted towards exploring its applications. Alongside the rise of artificial intelligence, various machine learning methods have been developed into quantum…

Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding…

Graph neural networks (GNNs) have become crucial in multimodal recommendation tasks because of their powerful ability to capture complex relationships between neighboring nodes. However, increasing the number of propagation layers in GNNs…

We study the optimization of wide neural networks (NNs) via gradient flow (GF) in setups that allow feature learning while admitting non-asymptotic global convergence guarantees. First, for wide shallow NNs under the mean-field scaling and…

Goal-conditioned reinforcement learning (GCRL) has a wide range of potential real-world applications, including manipulation and navigation problems in robotics. Especially in such robotics tasks, sample efficiency is of the utmost…

Multi-Agent Reinforcement Learning (MARL) struggles with sample inefficiency and poor generalization [1]. These challenges are partially due to a lack of structure or inductive bias in the neural networks typically used in learning the…

Global machine learning force fields (MLFFs), that have the capacity to capture collective many-atom interactions in molecular systems, currently only scale up to a few dozen atoms due a considerable growth of the model complexity with…

By leveraging neural networks, the emerging field of scientific machine learning (SciML) offers novel approaches to address complex problems governed by partial differential equations (PDEs). In practical applications, challenges arise due…

Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common…

Physics-constrained neural networks are commonly employed to enhance prediction robustness compared to purely data-driven models, achieved through the inclusion of physical constraint losses during the model training process. However, one…

This paper presents a proper generalized decomposition (PGD) based reduced-order model of hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-PGD method keeps both advantages of HiDeNN and PGD methods. The automatic…

Objective: Multi-modal functional magnetic resonance imaging (fMRI) can be used to make predictions about individual behavioral and cognitive traits based on brain connectivity networks. Methods: To take advantage of complementary…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…

We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…

Hypergraph neural networks (HGNNs) effectively model complex high-order relationships in domains like protein interactions and social networks by connecting multiple vertices through hyperedges, enhancing modeling capabilities, and reducing…

We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures…