Output Reachable Set Estimation and Verification for Multilayer Neural Networks

Weiming Xiang, Hoang Dung Tran, Taylor T. Johnson

Research output: Contribution to journalArticlepeer-review

118 Scopus citations


In this brief, the output reachable estimation and safety verification problems for multilayer perceptron (MLP) neural networks are addressed. First, a conception called maximum sensitivity is introduced, and for a class of MLPs 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 the proposed approaches.

Original languageEnglish (US)
Article number8318388
Pages (from-to)5777-5783
Number of pages7
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number11
StatePublished - Nov 2018
Externally publishedYes


  • Multilayer perceptron (MLP)
  • reachable set estimation
  • simulation
  • verification

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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