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In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…
Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and…
While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…
In this era of artificial intelligence, deep neural networks like Convolutional Neural Networks (CNNs) have emerged as front-runners, often surpassing human capabilities. These deep networks are often perceived as the panacea for all…
In this paper, we propose a novel Convolutional Neural Network (CNN) structure for general-purpose multi-task learning (MTL), which enables automatic feature fusing at every layer from different tasks. This is in contrast with the most…
While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…
Traditional convolutional layers extract features from patches of data by applying a non-linearity on an affine function of the input. We propose a model that enhances this feature extraction process for the case of sequential data, by…
Building large models with parameter sharing accounts for most of the success of deep convolutional neural networks (CNNs). In this paper, we propose doubly convolutional neural networks (DCNNs), which significantly improve the performance…
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…
Compared to earlier multistage frameworks using CNN features, recent end-to-end deep approaches for fine-grained recognition essentially enhance the mid-level learning capability of CNNs. Previous approaches achieve this by introducing an…
Convolutional architectures have recently been shown to be competitive on many sequence modelling tasks when compared to the de-facto standard of recurrent neural networks (RNNs), while providing computational and modeling advantages due to…
Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…
A theory of neural networks (NNs) built upon collective variables would provide scientists with the tools to better understand the learning process at every stage. In this work, we introduce two such variables, the entropy and the trace of…
In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain…
Convolutional Neural Networks (CNNs) are now a well-established tool for solving computational imaging problems. Modern CNN-based algorithms obtain state-of-the-art performance in diverse image restoration problems. Furthermore, it has been…
We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data, including images, point clouds, graphs,…
Deep learning has been demonstrated to achieve excellent results for image classification and object detection. However, the impact of deep learning on video analysis (e.g. action detection and recognition) has been limited due to…
In Convolutional Neural Network (CNN) based image processing, most studies propose networks that are optimized to single-level (or single-objective); thus, they underperform on other levels and must be retrained for delivery of optimal…