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Graph Convolutional Networks (GCNs) have been shown to be a powerful concept that has been successfully applied to a large variety of tasks across many domains over the past years. In this work we study the theory that paved the way to the…
Ground-to-aerial geolocalization refers to localizing a ground-level query image by matching it to a reference database of geo-tagged aerial imagery. This is very challenging due to the huge perspective differences in visual appearances and…
Even though Deep Neural Networks (DNNs) are widely celebrated for their practical performance, they possess many intriguing properties related to depth that are difficult to explain both theoretically and intuitively. Understanding how…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to…
We study the problem of deep joint source-channel coding (D-JSCC) for correlated image sources, where each source is transmitted through a noisy independent channel to the common receiver. In particular, we consider a pair of images…
This is the second in the series of papers on transport phenomena along random rough surfaces. We apply our simple general approach\cite{r1} to transport in very narrow channels, when the particles wavelength is comparable to the width of…
Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness on graph-based tasks. However, their predictive confidence is often miscalibrated, typically exhibiting under-confidence, which harms the reliability of their…
Graph neural networks (GNN) have shown great advantages in many graph-based learning tasks but often fail to predict accurately for a task-based on sets of nodes such as link/motif prediction and so on. Many works have recently proposed to…
The electronic states of an electrostatically confined cylindrical graphene quantum dot and the electric transport through this device are studied theoretically within the continuum Dirac-equation approximation and compared with numerical…
The original design of Graph Convolution Network (GCN) couples feature transformation and neighborhood aggregation for node representation learning. Recently, some work shows that coupling is inferior to decoupling, which supports deep…
A far-reaching goal of graphene research is exploiting the unique properties of carriers to realize extreme nonclassical electronic transport. Of particular interest is harnessing wavelike carriers to guide and direct them on submicron…
We present a novel methodology that combines graph and dense segmentation techniques by jointly learning both point and pixel contour representations, thereby leveraging the benefits of each approach. This addresses deficiencies in typical…
The path signature, having enjoyed recent success in the machine learning community, is a theoretically-driven method for engineering features from irregular paths. On the other hand, graph neural networks (GNN), neural architectures for…
We fabricate a graphene p-n-p heterojunction and exploit the coherence of weakly-confined Dirac quasiparticles to resolve the underlying scattering potential using low temperature scanning gate microscopy. The tip-induced perturbation to…
The Hessian of neural networks can be decomposed into a sum of two matrices: (i) the positive semidefinite generalized Gauss-Newton matrix G, and (ii) the matrix H containing negative eigenvalues. We observe that for wider networks,…
We present a Langlands dual realization of the putative category of affine character sheaves. Namely, we calculate the categorical center and trace (also known as the Drinfeld center and trace, or categorical Hochschild cohomology and…
We study the map learned by a family of autoencoders trained on MNIST, and evaluated on ten different data sets created by the random selection of pixel values according to ten different distributions. Specifically, we study the eigenvalues…
Due to their unique electrical properties, graphene nanoribbons (GNRs) show great promise as the building blocks of novel electronic devices. However, these properties are strongly dependent on the geometry of the edges of the graphene…
While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform…