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Research Group Matthias Althoff

Link to Matthias Althoff

Matthias Althoff

Prof. Dr.

Principal Investigator

Cyber Physical Systems

B3 | Multimodal Perception

Matthias Althoff

is Professor of Cyber Physical Systems at TU Munich.

His research interests lie in systems whose computations are closely connected with their physical behavior. Referred to as cyber-physical systems, these systems require an integrated approach applying methods from computer science and engineering. Examples of such systems are autonomous vehicles, smart grids, intelligent production systems and medical robotics. Stefan Bauer's research primarily focuses on formal methods for guaranteeing safety and correct operation as well as the model-based design of cyber-physical systems.

Team members @MCML

Link to Michael Eichelbeck

Michael Eichelbeck

Cyber Physical Systems

B3 | Multimodal Perception

Link to Philipp Gassert

Philipp Gassert

Cyber Physical Systems

B3 | Multimodal Perception

Link to Hanna Krasowski

Hanna Krasowski

Cyber Physical Systems

B3 | Multimodal Perception

Link to Jonathan Külz

Jonathan Külz

Cyber Physical Systems

B3 | Multimodal Perception

Link to Tobias Ladner

Tobias Ladner

Cyber Physical Systems

B3 | Multimodal Perception

Link to Laura Lützow

Laura Lützow

Cyber Physical Systems

B3 | Multimodal Perception

Publications @MCML

[2]
T. Ladner and M. Althoff.
Exponent Relaxation of Polynomial Zonotopes and Its Applications in Formal Neural Network Verification.
38th Conference on Artificial Intelligence (AAAI 2024). Vancouver, Canada, Feb 20-27, 2024. DOI.
Abstract

Formal verification of neural networks is a challenging problem due to the complexity and nonlinearity of neural networks. It has been shown that polynomial zonotopes can tightly enclose the output set of a neural network. Unfortunately, the tight enclosure comes with additional complexity in the set representation, thus, rendering subsequent operations expensive to compute, such as computing interval bounds and intersection checking. To address this issue, we present a novel approach to restructure a polynomial zonotope to tightly enclose the original polynomial zonotope while drastically reducing its complexity. The restructuring is achieved by relaxing the exponents of the dependent factors of polynomial zonotopes and finding an appropriate approximation error. We demonstrate the applicability of our approach on output sets of neural networks, where we obtain tighter results in various subsequent operations, such as order reduction, zonotope enclosure, and range bounding.

MCML Authors
Link to Tobias Ladner

Tobias Ladner

Cyber Physical Systems

B3 | Multimodal Perception

Link to Matthias Althoff

Matthias Althoff

Prof. Dr.

Cyber Physical Systems

B3 | Multimodal Perception


[1]
T. Ladner and M. Althoff.
Automatic Abstraction Refinement in Neural Network Verification Using Sensitivity Analysis.
26th ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2023). San Antonio, TX, USA, May 09-12, 2023. DOI.
Abstract

The formal verification of neural networks is essential for their application in safety-critical environments. However, the set-based verification of neural networks using linear approximations often obtains overly conservative results, while nonlinear approximations quickly become computationally infeasible in deep neural networks. We address this issue for the first time by automatically balancing between precision and computation time without splitting the propagated set. Our work introduces a novel automatic abstraction refinement approach using sensitivity analysis to iteratively reduce the abstraction error at the neuron level until either the specifications are met or a maximum number of iterations is reached. Our evaluation shows that we can tightly over-approximate the output sets of deep neural networks and that our approach is up to a thousand times faster than a naive approach. We further demonstrate the applicability of our approach in closed-loop settings.

MCML Authors
Link to Tobias Ladner

Tobias Ladner

Cyber Physical Systems

B3 | Multimodal Perception

Link to Matthias Althoff

Matthias Althoff

Prof. Dr.

Cyber Physical Systems

B3 | Multimodal Perception