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Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks (1708.03322v2)

Published 9 Aug 2017 in cs.LG

Abstract: In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.

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Authors (3)
  1. Weiming Xiang (29 papers)
  2. Hoang-Dung Tran (16 papers)
  3. Taylor T. Johnson (49 papers)
Citations (284)

Summary

  • The paper introduces a maximum sensitivity method that transforms output reachable set estimation into a series of convex optimization problems for effective safety verification.
  • It leverages finite simulations and precise input discretization to comprehensively characterize neural network output behaviors in robotic systems.
  • The layer-by-layer analysis demonstrates scalability and paves the way for extending these verification methods to more complex neural architectures.

Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

The exploration of verification techniques in neural networks is a vital endeavor in the field of artificial intelligence, particularly concerning systems that require stringent safety assurances. The paper "Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks" by Weiming Xiang et al. addresses emergent issues in the verification of multi-layer perceptron neural networks, specifically through the prism of output reachable set estimation.

Overview of Contributions

This research explores the complex problem of estimating the output reachable sets and conducting safety verification of multi-layer perceptrons (MLPs). Central to their methodology is the concept of "maximum sensitivity," which provides a metric for the maximum deviation of outputs due to bounded disturbances in inputs. This approach transforms the challenge of estimating reachable sets into a series of convex optimization problems, operable layer-by-layer for MLPs with monotonic activation functions.

The paper's innovations extend to a simulation-based methodology wherein the finite simulations conducted on a neural network aid in estimating the full set of possible output values, covering the network's behavior across a predefined input space. This technique allows for an extensive characterization of the network's output, facilitating automated safety verification.

Numerical Results and Validation

The authors apply their methodology to MLPs used in robotic arm models, demonstrating the approach's utility in real-world applications. Through their examples, they illustrate how smaller discretization radii—alluding to increased precision in the input space—result in more accurate and safer estimations of output reachable sets. Computational efficiency is achieved by leveraging convex optimizations, evidenced by results showing satisfactory safety verifications executed with different levels of input discretization.

Implications on AI and Future Directions

The theoretical and practical implications of this research are substantial. By establishing a method to estimate output reachable sets using maximum sensitivity, the paper provides a scalable framework that can potentially extend to more complex neural network architectures and safety-critical applications. The authors suggest that, while their current approach is effective for MLPs with monotonic activation functions, future investigations might consider extending these techniques to networks with non-monotonic elements or other structures like recurrent networks.

Moreover, the application of this work to real-world systems such as robotic arms demonstrates its applicability to adaptive control and automation domains, where safety is paramount. The potential for these methods to inform robust design and verification processes across these fields is significant.

Conclusion

Xiang et al.'s contribution marks progress in the assurance of neural network robustness and safety—a topic that is critical as AI systems are deployed in increasingly complex and safety-sensitive environments. This paper is a well-balanced mix of theoretical exploration and practical illustration, advancing the discourse around verification methods in neural systems. As the field of AI continues evolving, methodologies like those presented in this work will be crucial for the development of safe, reliable, and trustworthy systems.