Search Results for author: Philipp Christian Petersen

Found 7 papers, 2 papers with code

Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks

1 code implementation23 Apr 2024 Adeyemi D. Adeoye, Philipp Christian Petersen, Alberto Bemporad

This work studies a GGN method for optimizing a two-layer neural network with explicit regularization.

Mathematical Capabilities of ChatGPT

2 code implementations NeurIPS 2023 Simon Frieder, Luca Pinchetti, Alexis Chevalier, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Christian Petersen, Julius Berner

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, as well as hand-crafted ones, using a novel methodology.

Elementary Mathematics Math +2

VC dimensions of group convolutional neural networks

no code implementations19 Dec 2022 Philipp Christian Petersen, Anna Sepliarskaia

We study the generalization capacity of group convolutional neural networks.

Limitations of neural network training due to numerical instability of backpropagation

no code implementations3 Oct 2022 Clemens Karner, Vladimir Kazeev, Philipp Christian Petersen

We study the training of deep neural networks by gradient descent where floating-point arithmetic is used to compute the gradients.

Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems

no code implementations2 Jun 2022 Andrés Felipe Lerma Pineda, Philipp Christian Petersen

We demonstrate the admissibility of this approach to a wide range of inverse problems of practical interest.

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