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This work starts with the intention of using mathematics to understand the intriguing vulnerability observed by ~\citet{szegedy2013} within artificial neural networks. Along the way, we will develop some novel tools with applications far…
In standard generative deep learning models, such as autoencoders or GANs, the size of the parameter set is proportional to the complexity of the generated data distribution. A significant challenge is to deploy resource-hungry deep…
Biological neural networks have evolved to maintain performance despite significant circuit damage. To survive damage, biological network architectures have both intrinsic resilience to component loss and also activate recovery programs…
Anomaly detection is a crucial machine-learning task with wide-ranging applications. Deep Support Vector Data Description (Deep SVDD) is a prominent deep one-class method, but it is vulnerable to hypersphere collapse, often relies on…
Domain adaptation remains a challenge when there is significant manifold discrepancy between source and target domains. Although recent methods leverage manifold-aware adversarial perturbations to perform data augmentation, they often…
Accurate brain tumor segmentation from MRI scans is critical for diagnosis and treatment planning. Despite the strong performance of recent deep learning approaches, two fundamental limitations remain: (1) the lack of reliable uncertainty…
Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their…
Objective: Recognizing retinal vessel abnormity is vital to early diagnosis of ophthalmological diseases and cardiovascular events. However, segmentation results are highly influenced by elusive vessels, especially in low-contrast…
Minerals detection over large volume of spectra is the challenge addressed by current hyperspectral imaging spectrometer in Planetary Science. Instruments such OMEGA (Mars Express), CRISM (Mars Reconnaissance Orbiter), M^{3}…
Heterogeneous information networks (HINs) have been extensively applied to real-world tasks, such as recommendation systems, social networks, and citation networks. While existing HIN representation learning methods can effectively learn…
With the development of deep learning, Deep Metric Learning (DML) has achieved great improvements in face recognition. Specifically, the widely used softmax loss in the training process often bring large intra-class variations, and feature…
There has been considerable effort to better understand the generalization capabilities of deep neural networks both as a means to unlock a theoretical understanding of their success as well as providing directions for further improvements.…
High fidelity segmentation of both macro and microvascular structure of the retina plays a pivotal role in determining degenerative retinal diseases, yet it is a difficult problem. Due to successive resolution loss in the encoding phase…
Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do…
We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…
Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression…
Graph neural networks have shown promising results in weather forecasting, which is critical for human activity such as agriculture planning and extreme weather preparation. However, most studies focus on finite and local areas for…
The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Deformable registration consists of finding the best dense correspondence between two different images. Many algorithms have been published, but the clinical application was made difficult by the high calculation time needed to solve the…