Related papers: SurReal: Complex-Valued Learning as Principled Tra…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

This paper introduces a novel approach that combines unsupervised active contour models with deep learning for robust and adaptive image segmentation. Indeed, traditional active contours, provide a flexible framework for contour evolution…

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…

Artificial neural networks (ANNs) based machine learning models and especially deep learning models have been widely applied in computer vision, signal processing, wireless communications, and many other domains, where complex numbers occur…

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind…

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal…

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension…

Image segmentation is the process of partitioning a image into different regions or groups based on some characteristics like color, texture, motion or shape etc. Active contours is a popular variational method for object segmentation in…

Fairness in machine learning is increasingly critical, yet standard approaches often treat data as static points in a high-dimensional space, ignoring the underlying generative structure. We posit that sensitive attributes (e.g., race,…

Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Convolutional neural networks (CNNs) are the cutting edge model for supervised machine learning in computer vision. In recent years CNNs have outperformed traditional approaches in many computer vision tasks such as object detection, image…

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…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

The inherently complex-valued nature of Polarimetric SAR data necessitates using specialized algorithms capable of directly processing complex-valued representations. However, this aspect remains underexplored in the deep learning…

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…

Molecular representations fundamentally shape how machine learning systems reason about molecular structure and physical properties. Most existing approaches adopt a discrete pipeline: molecules are encoded as sequences, graphs, or point…

Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of message passing in this field, it has limitations such as…