33,390 research outputs found
Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks
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.Comment: 8 pages, 9 figures, to appear in TNNL
Fast Quantum Algorithm for Solving Multivariate Quadratic Equations
In August 2015 the cryptographic world was shaken by a sudden and surprising
announcement by the US National Security Agency NSA concerning plans to
transition to post-quantum algorithms. Since this announcement post-quantum
cryptography has become a topic of primary interest for several standardization
bodies. The transition from the currently deployed public-key algorithms to
post-quantum algorithms has been found to be challenging in many aspects. In
particular the problem of evaluating the quantum-bit security of such
post-quantum cryptosystems remains vastly open. Of course this question is of
primarily concern in the process of standardizing the post-quantum
cryptosystems. In this paper we consider the quantum security of the problem of
solving a system of {\it Boolean multivariate quadratic equations in
variables} (\MQb); a central problem in post-quantum cryptography. When ,
under a natural algebraic assumption, we present a Las-Vegas quantum algorithm
solving \MQb{} that requires the evaluation of, on average,
quantum gates. To our knowledge this is the fastest algorithm for solving
\MQb{}
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