Related papers: The Volterra signature
In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the…
Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of…
One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…
Implicit Neural Representations (INRs) have emerged as a powerful paradigm for parameterizing physical fields, yet they often suffer from spectral bias and the computational expense of non-convex optimization. We introduce the Vekua Layer…
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…
Our current understanding of the structure and dynamics of aqueous interfaces at the molecular level has grown substantially in the last few decades due to the continuous development of surface-specific spectroscopies, such as vibrational…
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…
Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular,…
This work concerns the analysis of the discontinuous Galerkin spectral element method (DGSEM) with implicit time stepping for the numerical approximation of nonlinear scalar conservation laws in multiple space dimensions. We consider either…
This paper addresses a new class of generalized Bolza problems governed by nonconvex integro-differential inclusions with endpoint constraints on trajectories, where the integral terms are given in the general (with time-dependent…
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…
Implicit representation of shapes as level sets of multilayer perceptrons has recently flourished in different shape analysis, compression, and reconstruction tasks. In this paper, we introduce an implicit neural representation-based…
Path signatures embed trajectories into tensor algebra and constitute a universal, non-parametric representation of paths; however, in the standard form, they collapse temporal structure into a single global object, which limits their…
This paper derives a new class of vector-valued reproducing kernel Hilbert spaces (vRKHS) defined in terms of operator-valued kernels for the representation of functional uncertainty arising in nonparametric adaptive control methods. These…
Temporal Knowledge Graphs (TKGs) store temporal facts with quadruple formats (s, p, o, t). Existing Temporal Knowledge Graph Embedding (TKGE) models perform link prediction tasks in transductive or semi-inductive settings, which means the…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling…
We study the Lotka--Volterra system from the perspective of computational algebraic geometry, focusing on equilibria that are both feasible and stable. These conditions stratifies the parameter space in $\mathbb{R}\times\mathbb{R}^{n\times…
Learning object manipulation is a critical skill for robots to interact with their environment. Even though there has been significant progress in robotic manipulation of rigid objects, interacting with non-rigid objects remains challenging…
In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex particles, hurdling the Lagrangian particles from inheriting…