3 citations · 4 across the 9 of their papers we have counts for
10 papers
On Unstable Fixed Points in Modern Continuous Hopfield Networks
Hans-Peter Beise
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule --…
Hyperplane Arrangements and Fixed Points in Iterated PWL Neural Networks
Hans-Peter Beise
We leverage the framework of hyperplane arrangements to analyze potential regions of (stable) fixed points. We provide an upper bound on the number of fixed points for multi-layer…
Topological properties of basins of attraction and expressiveness of width bounded neural networks
Hans-Peter Beise, Steve Dias Da Cruz
In Radhakrishnan et al. [2020], the authors empirically show that autoencoders trained with usual SGD methods shape out basins of attraction around their training data. We consider…
A Hybrid Objective Function for Robustness of Artificial Neural Networks -- Estimation of Parameters in a Mechanical System
Jan Sokolowski, Volker Schulz, Udo Schröder +1
In several studies, hybrid neural networks have proven to be more robust against noisy input data compared to plain data driven neural networks. We consider the task of estimating…
SVIRO: Synthetic Vehicle Interior Rear Seat Occupancy Dataset and Benchmark
Steve Dias Da Cruz, Oliver Wasenmüller, Hans-Peter Beise +2
We release SVIRO, a synthetic dataset for sceneries in the passenger compartment of ten different vehicles, in order to analyze machine learning-based approaches for their generali…
Mixing operators with prescribed unimodular eigenvectors
Hans-Peter Beise, Leonhard Frerick, Jürgen Müller
For arbitrary closed countable subsets of the unit circle examples of topologically mixing operators on Hilbert spaces are given which have a densely spanning set of unimodular…
On decision regions of narrow deep neural networks
Hans-Peter Beise, Steve Dias Da Cruz, Udo Schröder
We show that for neural network functions that have width less or equal to the input dimension all connected components of decision regions are unbounded. The result holds for cont…
Generic boundary behaviour of Taylor series in Hardy and Bergman spaces
Hans-Peter Beise, Jürgen Müller
It is known that, generically, Taylor series of functions holomorphic in the unit disc turn out to be universal series outside of the unit disc and in particular on the unit circle…
On the intersection of the spectrum of frequently hypercyclic operators with the unit circle
Hans-Peter Beise
We exclude the existence of frequently hypercyclic operators that have a spectrum contained in the closed unit disc and that intersects the unit circle in only finitely many points…
Growth of frequently Birkhoff-universal functions of exponential type on rays
Hans-Peter Beise
We consider growth conditions for (frequently) Birkhoff-universal functions of exponential type with respect to the different rays emanating from the origin. For that purpose, we i…