302 citations · 305 across the 6 of their papers we have counts for
6 papers
Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networks
Clemens Kinn, Philipp Petersen
We study binary classification problems whose decision sets are given by definable sets in o-minimal expansions of the real field. Motivated by cell decomposition of definable sets…
Minimax learning rates for estimating binary classifiers under margin conditions
Jonathan García, Philipp Petersen
We study classification problems using binary estimators where the decision boundary is described by horizon functions and where the data distribution satisfies a geometric margin…
High-dimensional classification problems with Barron regular boundaries under margin conditions
Jonathan García, Philipp Petersen
We prove that a classifier with a Barron-regular decision boundary can be approximated with a rate of high polynomial degree by ReLU neural networks with three hidden layers when a…
Dimension-independent learning rates for high-dimensional classification problems
Andres Felipe Lerma-Pineda, Philipp Petersen, Simon Frieder +1
We study the problem of approximating and estimating classification functions that have their decision boundary in the space. Functions of type arise naturally as s…
Large Language Models for Mathematicians
Simon Frieder, Julius Berner, Philipp Petersen +1
Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-qual…
Mathematical Capabilities of ChatGPT
Simon Frieder, Luca Pinchetti, Alexis Chevalier +5
We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets,…