5 papers
SensLI: Sensitivity-Based Layer Insertion for Neural Networks
Leonie Kreis, Evelyn Herberg, Frederik Köhne +2
The training of neural networks requires tedious and often manual tuning of the network architecture. We propose a systematic approach to inserting new layers during the training p…
An Exponential Averaging Process with Strong Convergence Properties
Frederik Köhne, Anton Schiela
Averaging, or smoothing, is a fundamental approach to obtain stable, de-noised estimates from noisy observations. In certain scenarios, observations made along trajectories of rand…
Adaptive Step Sizes for Preconditioned Stochastic Gradient Descent
Frederik Köhne, Leonie Kreis, Anton Schiela +1
This paper proposes a novel approach to adaptive step sizes in stochastic gradient descent (SGD) by utilizing quantities that we have identified as numerically traceable -- the Lip…
Nonlinear Fenchel Conjugates
Anton Schiela, Roland Herzog, Ronny Bergmann
The classical concept of Fenchel conjugation is tailored to extended real-valued functions defined on linear spaces. In this paper we generalize this concept to functions defined o…
-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition
Frederik Köhne, Friedrich M. Philipp, Manuel Schaller +2
Extended dynamic mode decomposition (EDMD) is a well-established method to generate a data-driven approximation of the Koopman operator for analysis and prediction of nonlinear dyn…