Related papers: Integral Value Transformations: A Class of Discret…

This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…

Value Iteration Networks (VINs) have emerged as a popular method to incorporate planning algorithms within deep reinforcement learning, enabling performance improvements on tasks requiring long-range reasoning and understanding of…

Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…

We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as…

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric…

We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…

Disentanglement learning is central to understanding and reusing learned representations in variational autoencoders (VAEs). Although equivariance has been explored in this context, effectively exploiting it for disentanglement remains…

This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…

Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have…

There still remains an extreme performance gap between Vision Transformers (ViTs) and Convolutional Neural Networks (CNNs) when training from scratch on small datasets, which is concluded to the lack of inductive bias. In this paper, we…

Topology of the isospectral variety of zero-diagonal Jacobi matrices is investigated using the Volterra system.

Vision Transformers (ViTs) are normally regarded as a stack of transformer layers. In this work, we propose a novel view of ViTs showing that they can be seen as ensemble networks containing multiple parallel paths with different lengths.…

Recent interest in exploring local vacuum structure of QCD through the properties of the eigenmodes of the lattice Dirac operators rises again the challenge to visualize four-dimensional objects and structures which appear in lattice field…

This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being…

Computational Pathology (CPATH) systems have the potential to automate diagnostic tasks. However, the artifacts on the digitized histological glass slides, known as Whole Slide Images (WSIs), may hamper the overall performance of CPATH…

Deep neural networks (DNNs) have transformed fields such as computer vision and natural language processing by employing architectures aligned with domain-specific structural patterns. In algorithmic trading, however, there remains a lack…

The emergence of vision transformers (ViTs) in image classification has shifted the methodologies for visual representation learning. In particular, ViTs learn visual representation at full receptive field per layer across all the image…

In recent years, Transformer-based architectures have become the dominant method for Computer Vision applications. While Transformers are explainable and scale well with dataset size, they lack the inductive biases of Convolutional Neural…

Traditionally, shape transformation using implicit functions is performed in two distinct steps: 1) creating two implicit functions, and 2) interpolating between these two functions. We present a new shape transformation method that…