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A desireable property of accelerometric gait-based identification systems is robustness to new device orientations presented by users during testing but unseen during the training phase. However, traditional Convolutional neural networks…
We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}_2$ [1] to position-orientation space $\mathbb{M}_2 \cong \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance and…
Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to…
When seeing a new object, humans can immediately recognize it across different retinal locations: the internal object representation is invariant to translation. It is commonly believed that Convolutional Neural Networks (CNNs) are…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
The puzzle of computer vision might find new challenging solutions when we realize that most successful methods are working at image level, which is remarkably more difficult than processing directly visual streams. In this paper, we claim…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
Neural channel decoder, as a data-driven channel decoding strategy, has shown very promising improvement on error-correcting capability over the classical methods. However, the success of those deep learning-based decoder comes at the cost…
Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compactly supported stencils and point-wise nonlinearities. Commonly, the convolution operators couple features from all…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
Non-linear spectral decompositions of images based on one-homogeneous functionals such as total variation have gained considerable attention in the last few years. Due to their ability to extract spectral components corresponding to objects…
When seeing a new object, humans can immediately recognize it across different retinal locations: we say that the internal object representation is invariant to translation. It is commonly believed that Convolutional Neural Networks (CNNs)…
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…
Neural network (connectionist) models are designed to encode image features and provide the building blocks for object and shape recognition. These models generally call for: a) initial diffuse connections from one neuron population to…
Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the…
Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…