Related papers: Geometric Scattering on Manifolds
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…
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…
Imaging with optical resolution through highly scattering media is a long sought-after goal with important applications in deep tissue imaging. Although being the focus of numerous works, this goal was considered impractical until recently.…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…
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…
Convolutional neural networks (CNNs), in a few decades, have outperformed the existing state of the art methods in classification context. However, in the way they were formalised, CNNs are bound to operate on euclidean spaces. Indeed,…
Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a…
The prediction of salient areas in images has been traditionally addressed with hand-crafted features based on neuroscience principles. This paper, however, addresses the problem with a completely data-driven approach by training a…
Despite the success of deep learning on representing images for particular object retrieval, recent studies show that the learned representations still lie on manifolds in a high dimensional space. This makes the Euclidean nearest neighbor…
We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…
This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…
We use the scattering network as a generic and fixed ini-tialization of the first layers of a supervised hybrid deep network. We show that early layers do not necessarily need to be learned, providing the best results to-date with…
Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…
Precipitation nowcasting (up to a few hours) remains a challenge due to the highly complex local interactions that need to be captured accurately. Convolutional Neural Networks rely on convolutional kernels convolving with grid data and the…
Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in…
Invariant scattering transform introduces new area of research that merges the signal processing with deep learning for computer vision. Nowadays, Deep Learning algorithms are able to solve a variety of problems in medical sector. Medical…
Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our understanding of neural feature representations is still…
Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…
This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…
As the demand for user privacy grows, controlled data removal (machine unlearning) is becoming an important feature of machine learning models for data-sensitive Web applications such as social networks and recommender systems.…