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Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

Recently proposed Gated Linear Networks present a tractable nonlinear network architecture, and exhibit interesting capabilities such as learning with local error signals and reduced forgetting in sequential learning. In this work, we…

In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…

In this paper, we revisit the classical representation of 3D point clouds as linear shape models. Our key insight is to leverage deep learning to represent a collection of shapes as affine transformations of low-dimensional linear shape…

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…

We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Graph neural networks (GNNs), as topology/structure-aware models within deep learning, have emerged as powerful tools for AI-aided drug discovery (AIDD). By directly operating on molecular graphs, GNNs offer an intuitive and expressive…

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…

Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds. However, conventional encoding does not include angular information, which is critical for…

In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…

We study the Riemannian geometry of the Deep Linear Network (DLN) as a foundation for a thermodynamic description of the learning process. The main tools are the use of group actions to analyze overparametrization and the use of Riemannian…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional…

There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used…

With the recent advance of geometric deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of…

We present a novel unsupervised deep learning framework for anomalous event detection in complex video scenes. While most existing works merely use hand-crafted appearance and motion features, we propose Appearance and Motion DeepNet (AMDN)…

Advancements in deep learning are revolutionizing science and engineering. The immense success of deep learning is largely due to its ability to extract essential high-dimensional (HD) features from input data and make inference decisions…

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the…