Formal Verification of Robustness and Resilience in Learning-Enabled State Estimation Systems

Core Concepts

This paper presents a formal verification approach to assess the robustness and resilience of learning-enabled state estimation systems, which integrate neural networks and Bayes filters. It formalizes the concepts of robustness and resilience, reduces the learning-enabled systems to a novel class of labeled transition systems, and develops automated verification algorithms to check the satisfiability of these properties.

Abstract

The paper focuses on learning-enabled state estimation systems (LE-SESs), which are widely used in robotics applications to determine the current state of a complex system. LE-SESs integrate neural networks for processing sensory input and Bayes filters for state estimation.
The key highlights are:

Formal definitions of robustness and resilience for LE-SESs are provided, distinguishing them from the general concepts used in software engineering.
LE-SESs are reduced to a novel class of labeled transition systems called {PO}2-LTS, which captures the payoffs and partial order relations between transitions.
The verification of robustness and resilience properties on LE-SESs is formulated as constrained optimization problems over {PO}2-LTS, and it is proven to be NP-complete.
An automated verification algorithm is developed to check the satisfiability of robustness and resilience properties, and to provide representative examples.
A real-world WAMI dynamic tracking system is used as a case study, where the formal verification approach guides the design of a more robust and resilient LE-SES.

Stats

The paper does not contain explicit numerical data or statistics. It focuses on the formal modeling and verification of robustness and resilience properties.

Quotes

"Robustness is an enforced measure to represent a system's ability to consistently deliver its expected functionality by accommodating disturbances to the input."
"Resilience indicates an innate capability to maintain or recover sufficient functionality in the face of challenging conditions against risk or uncertainty, while keeping a certain level of vitality and prosperity."

Key Insights Distilled From

Formal Verification of Robustness and Resilience of Learning-Enabled State Estimation Systems

by Wei Huang,Yi... at arxiv.org 04-01-2024

https://arxiv.org/pdf/2010.08311.pdf

Deeper Inquiries

How can the formal verification approach be extended to handle other types of learning-enabled systems beyond state estimation

To extend the formal verification approach to handle other types of learning-enabled systems beyond state estimation, we can adapt the {PO}2-LTS model to accommodate the specific characteristics and requirements of those systems. For instance, for systems involving natural language processing or speech recognition, the model can be modified to incorporate the processing of textual or audio data. This may involve defining new transition rules, labelling functions, and payoff functions tailored to the unique features of the system. Additionally, the constraints for formal properties such as robustness and resilience can be redefined to suit the objectives and challenges of the particular learning-enabled system under consideration.

What are the potential limitations of the current {PO}2-LTS model, and how can it be further improved to capture more complex system behaviors

The current {PO}2-LTS model may have limitations in capturing more complex system behaviors due to its simplifications and assumptions. One potential limitation is the assumption of linear relationships between states and observations, which may not hold in systems with nonlinear dynamics. To improve the model, nonlinear relationships can be incorporated, allowing for a more accurate representation of system behavior. Additionally, the model could be enhanced by considering probabilistic transitions and uncertainties in a more detailed manner. This would provide a more realistic depiction of the system's dynamics and improve the accuracy of formal verification results.

What are the implications of the distinction between robustness and resilience for the design and deployment of safety-critical autonomous systems

The distinction between robustness and resilience has significant implications for the design and deployment of safety-critical autonomous systems. Robustness focuses on the system's ability to maintain expected functionality in the presence of disturbances, such as adversarial attacks, while resilience emphasizes the system's capacity to recover and adapt to challenging conditions. Understanding this distinction is crucial for designing systems that can withstand unexpected events and continue to operate effectively.
In practice, this means that safety-critical autonomous systems need to be designed with both robustness and resilience in mind. Robustness measures can help prevent system failures under normal operating conditions, while resilience measures can ensure that the system can recover from disruptions and continue to function in adverse situations. By incorporating both aspects into the design process, engineers can create systems that are better equipped to handle uncertainties and maintain safety and reliability in dynamic environments.