arXiv subjects

Niklas Weber

Publications and source records attributed to Niklas Weber.

4 recordsLinked to original sources

arXiv2026

Universality and Approximation Rates of Graph Neural Networks with Random Features

We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically. Here, we establish a novel universality result focusing on permutation-equivariant neural networks (PENNs), a class of GNNs built from feedforward neural network components that subsumes many prominent GNN architectures. We show that PENNs, combined with partially random node features, can approximate arbitrarily well in probability any measurable permutation-invariant or permutation-equivariant function on directed graphs of fixed size with multidimensional node and edge features. For $k$-times continuously differentiable functions, $k\geq 2$, we also derive upper bounds on the approximation rates, relating the complexity of the feedforward components of a PENN in terms of layer depth and number of nonzero weights to the desired approximation accuracy.

cs.LG↗

arXiv2024

Computing Systemic Risk Measures with Graph Neural Networks

This paper investigates systemic risk measures for stochastic financial networks of explicitly modelled bilateral liabilities. We extend the notion of systemic risk measures from Biagini, Fouque, Fritelli and Meyer-Brandis (2019) to graph structured data. In particular, we focus on an aggregation function that is derived from a market clearing algorithm proposed by Eisenberg and Noe (2001). In this setting, we show the existence of an optimal random allocation that distributes the overall minimal bailout capital and secures the network. We study numerical methods for the approximation of systemic risk and optimal random allocations. We propose to use permutation equivariant architectures of neural networks like graph neural networks (GNNs) and a class that we name (extended) permutation equivariant neural networks ((X)PENNs). We compare their performance to several benchmark allocations. The main feature of GNNs and (X)PENNs is that they are permutation equivariant with respect to the underlying graph data. In numerical experiments we find evidence that these permutation equivariant methods are superior to other approaches.

q-fin.CP↗

arXiv2022

Extending Open Bandit Pipeline to Simulate Industry Challenges

Bandit algorithms are often used in the e-commerce industry to train Machine Learning (ML) systems when pre-labeled data is unavailable. However, the industry setting poses various challenges that make implementing bandit algorithms in practice non-trivial. In this paper, we elaborate on the challenges of off-policy optimisation, delayed reward, concept drift, reward design, and business rules constraints that practitioners at Booking.com encounter when applying bandit algorithms. Our main contributions is an extension to the Open Bandit Pipeline (OBP) framework. We provide simulation components for some of the above-mentioned challenges to provide future practitioners, researchers, and educators with a resource to address challenges encountered in the e-commerce industry.

cs.LG↗

arXiv2022

Friction on layered media: How deep do phonons reach?

We theoretically study the frictional damping of a small probe object on a coated planar surface, analyzing the resulting phonon modes via a theory of viscoelasticity. Three different types of excitations are found to contribute to friction in distinct ways: traveling (3D) spherical waves, traveling (2D) surface waves, and evanescent waves. While traveling waves transport energy away from the probe, determined by long range elastic properties (wavelength), evanescent waves transform energy into heat in a near-field range, characterized by the size of the probe. Thus, fundamentally different behaviors are predicted, depending on coating thickness and material properties.

cond-mat.stat-mech↗