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3D reconstruction is a longstanding ill-posed problem, which has been explored for decades by the computer vision, computer graphics, and machine learning communities. Since 2015, image-based 3D reconstruction using convolutional neural…

Deep artificial neural networks require a large corpus of training data in order to effectively learn, where collection of such training data is often expensive and laborious. Data augmentation overcomes this issue by artificially inflating…

Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…

To overcome the restriction of identical distribution assumption, invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities. In UDA…

Deep learning in molecular and materials sciences is limited by the lack of integration between applied science, artificial intelligence, and high-performance computing. Bottlenecks with respect to the amount of training data, the size and…

Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable…

Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…

Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning…

This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and…

Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…

Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances…

Grasping objects of different shapes and sizes - a foundational, effortless skill for humans - remains a challenging task in robotics. Although model-based approaches can predict stable grasp configurations for known object models, they…

Training deep graph neural networks (GNNs) is notoriously hard. Besides the standard plights in training deep architectures such as vanishing gradients and overfitting, it also uniquely suffers from over-smoothing, information squashing,…

Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…

Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…

This paper presents a general graph representation learning framework called DeepGL for learning deep node and edge representations from large (attributed) graphs. In particular, DeepGL begins by deriving a set of base features (e.g.,…

Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…