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Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…

The recent introduction of Graph Neural Networks (GNNs) and their growing popularity in the past few years has enabled the application of deep learning algorithms to non-Euclidean, graph-structured data. GNNs have achieved state-of-the-art…

We introduce the first neural optimization framework to solve a classical instance of the tiling problem. Namely, we seek a non-periodic tiling of an arbitrary 2D shape using one or more types of tiles: the tiles maximally fill the shape's…

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…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

The distance-geometric graph representation adopts a unified scheme (distance) for representing the geometry of three-dimensional(3D) graphs. It is invariant to rotation and translation of the graph and it reflects pair-wise node…

We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…

Deep neural networks can empirically perform efficient hierarchical learning, in which the layers learn useful representations of the data. However, how they make use of the intermediate representations are not explained by recent theories…

Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The…

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on…

Supervised learning techniques have proven their efficacy in many applications with abundant data. However, applying these methods to medical imaging is challenging due to the scarcity of data, given the high acquisition costs and intricate…

Deep RL approaches build much of their success on the ability of the deep neural network to generate useful internal representations. Nevertheless, they suffer from a high sample-complexity and starting with a good input representation can…

In this article we review computational aspects of Deep Learning (DL). Deep learning uses network architectures consisting of hierarchical layers of latent variables to construct predictors for high-dimensional input-output models. Training…

Graph Neural Networks (GNNs) are an emerging research field. This specialized Deep Neural Network (DNN) architecture is capable of processing graph structured data and bridges the gap between graph processing and Deep Learning (DL). As…

One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from observed data. In this work, we make one step towards…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…