Related papers: The Volterra signature
We consider a class of nonlocal conservation laws modeling traffic flow, given by $ \partial_t u_\varepsilon + \partial_x(V(u_\varepsilon \ast \gamma_\varepsilon)\, u_\varepsilon) = 0 $ with $ \gamma_\varepsilon(\cdot) :=…
The most popular graph indices for vector search use principles from computational geometry to build the graph. Hence, their formal graph navigability guarantees are only valid in Euclidean space. In this work, we show that machine learning…
Vector-space models, from word embeddings to neural network parsers, have many advantages for NLP. But how to generalise from fixed-length word vectors to a vector space for arbitrary linguistic structures is still unclear. In this paper we…
We consider the model equation arising in the theory of viscoelasticity $$\partial_{tt} u-h_t(0)\Delta u -\int_{0}^\infty h_t'(s)\Delta u(t-s)d s+ f(u) = g.$$ Here, the main feature is that the memory kernel $h_t(\cdot)$ depends on time,…
Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural…
We study the computational complexity of several polynomial-time-solvable graph problems parameterized by vertex integrity, a measure of a graph's vulnerability to vertex removal in terms of connectivity. Vertex integrity is the smallest…
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of…
Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the…
Neural networks have shown great promise in providing a data-first approach to exploring new physics. In this work, we use the full implementation of late time cosmological data to reconstruct a number of scalar-tensor cosmological models…
In this paper, we investigate and analyze numerical solutions for the Volterra integrodifferential equations with tempered multi-term kernels. Firstly we derive some regularity estimates of the exact solution. Then a temporal-discrete…
Support Vector Machines (SVMs) are well-established Machine Learning (ML) algorithms. They rely on the fact that i) linear learning can be formalized as a well-posed optimization problem; ii) non-linear learning can be brought into linear…
A faithful description of chemical processes requires exploring extended regions of the molecular potential energy surface (PES), which remains challenging for strongly correlated systems. Transferable deep-learning variational Monte Carlo…
A new alternative method to approximate the Visibility Graph (VG) of a time series has been introduced here. It exploits the fact that most of the nodes in the resulting network are not connected to those that are far away from them. This…
Knowledge graph (KG) inference aims to address the natural incompleteness of KGs, including rule learning-based and KG embedding (KGE) models. However, the rule learning-based models suffer from low efficiency and generalization while KGE…
Representing a signal as a continuous function parameterized by neural network (a.k.a. Implicit Neural Representations, INRs) has attracted increasing attention in recent years. Neural Processes (NPs), which model the distributions over…
This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the operational matrices of the Walsh function and the collocation method. The method transforms…
The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation…
The complete positivity, i.e., positivity of the resolvent kernels, for convolutional kernels is an important property for the positivity property and asymptotic behaviors of Volterra equations. We inverstigate the discrete analogue of the…
Support vector machines (SVMs) have been successful in solving many computer vision tasks including image and video category recognition especially for small and mid-scale training problems. The principle of these non-parametric models is…