7 papers
Operator Neural Jump ODEs: -optimal prediction in function spaces
Florian Krach, Oliver Löthgren, Josef Teichmann
In this paper, we study the extension of Neural Jump ODEs to infinite-dimensional function spaces. In particular, the underlying process now takes values in $L^2(Ξ, \mathbb{R}^…
Neural Jump ODEs as Generative Models
Robert A. Crowell, Florian Krach, Josef Teichmann
In this work, we explore how Neural Jump ODEs (NJODEs) can be used as generative models for Itô processes. Given (discrete observations of) samples of a fixed underlying Itô proces…
Revealing the temporal dynamics of antibiotic anomalies in the infant gut microbiome with neural jump ODEs
Anja Adamov, Markus Chardonnet, Florian Krach +3
Detecting anomalies in irregularly sampled multi-variate time-series is challenging, especially in data-scarce settings. Here we introduce an anomaly detection framework for irregu…
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of…
Universal approximation property of neural stochastic differential equations
Anna P. Kwossek, David J. Prömel, Josef Teichmann
We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neura…
Learning Chaotic Systems and Long-Term Predictions with Neural Jump ODEs
Florian Krach, Josef Teichmann
The Path-dependent Neural Jump ODE (PD-NJ-ODE) is a model for online prediction of generic (possibly non-Markovian) stochastic processes with irregular (in time) and potentially in…
Robust Utility Optimization via a GAN Approach
Florian Krach, Josef Teichmann, Hanna Wutte
Robust utility optimization enables an investor to deal with market uncertainty in a structured way, with the goal of maximizing the worst-case outcome. In this work, we propose a…