26 citations · 34 across the 8 of their papers we have counts for
10 papers
Complexity Theory meets Ordinary Differential Equations
Adalbert Fono, Noah Wedlich, Holger Boche +1
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization o…
The Price of Robustness: Stable Classifiers Need Overparameterization
Jonas von Berg, Adalbert Fono, Massimiliano Datres +2
The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by est…
Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time
Duc Anh Nguyen, Ernesto Araya, Adalbert Fono +1
Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural ne…
Sustainable AI: Mathematical Foundations of Spiking Neural Networks
Adalbert Fono, Manjot Singh, Ernesto Araya +3
Deep learning's success comes with growing energy demands, raising concerns about the long-term sustainability of the field. Spiking neural networks, inspired by biological neurons…
Computability of Classification and Deep Learning: From Theoretical Limits to Practical Feasibility through Quantization
Holger Boche, Vit Fojtik, Adalbert Fono +1
The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep l…
Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement
Holger Boche, Adalbert Fono, Gitta Kutyniok
Deep learning still has drawbacks in terms of trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obliga…
Expressivity of Spiking Neural Networks
Manjot Singh, Adalbert Fono, Gitta Kutyniok
The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications. Inspired by this potential, we revisit…
Turing meets Moore-Penrose: Computing the Pseudoinverse on Turing Machines
Holger Boche, Adalbert Fono, Gitta Kutyniok
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existe…
Inverse Problems Are Solvable on Real Number Signal Processing Hardware
Holger Boche, Adalbert Fono, Gitta Kutyniok
Despite the success of Deep Learning (DL) serious reliability issues such as non-robustness persist. An interesting aspect is, whether these problems arise due to insufficient tool…
Limitations of Deep Learning for Inverse Problems on Digital Hardware
Holger Boche, Adalbert Fono, Gitta Kutyniok
Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed…