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Dimensionality reduction methods, also known as projections, are frequently used for exploring multidimensional data in machine learning, data science, and information visualization. Among these, t-SNE and its variants have become very…
Generative models that produce point clouds have emerged as a powerful tool to represent 3D surfaces, and the best current ones rely on learning an ensemble of parametric representations. Unfortunately, they offer no control over the…
Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…
The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous…
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…
Optimizing fluid-dynamic performance is an important engineering task. Traditionally, experts design shapes based on empirical estimations and verify them through expensive experiments. This costly process, both in terms of time and space,…
We introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve…
We study neural network training (NNT): optimizing a neural network's parameters to minimize the training loss over a given dataset. NNT has been studied extensively under theoretic lenses, mainly on two-layer networks with linear or ReLU…
The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to…
Graph Convolutional Neural Networks (GCNNs) extend classical CNNs to graph data domain, such as brain networks, social networks and 3D point clouds. It is critical to identify an appropriate graph for the subsequent graph convolution.…
In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data…
Incorporation of prior knowledge about organ shape and location is key to improve performance of image analysis approaches. In particular, priors can be useful in cases where images are corrupted and contain artefacts due to limitations in…
Graph Neural Networks (GNNs) are deep-learning architectures designed for graph-type data, where understanding relationships among individual observations is crucial. However, achieving promising GNN performance, especially on unseen data,…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
Due to the significant computational challenge of training large-scale graph neural networks (GNNs), various sparse learning techniques have been exploited to reduce memory and storage costs. Examples include \textit{graph sparsification}…
Sketch-based modeling strives to bring the ease and immediacy of drawing to the 3D world. However, while drawings are easy for humans to create, they are very challenging for computers to interpret due to their sparsity and ambiguity. We…
Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…
Hypernetworks, or hypernets for short, are neural networks that generate weights for another neural network, known as the target network. They have emerged as a powerful deep learning technique that allows for greater flexibility,…
We use Deep Neural Networks (DNNs) to classify and reconstruct a large database of handwritten digits from the intensity of the speckle patterns that result after the images propagated through multimode fibers (MMF). Images transmitted…