2,173 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
LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural
networks from a dynamical system perspective. The classical recursive equations
describing the evolution of LSTM can be recast in state space form, resulting
in a time-invariant nonlinear dynamical system. A sufficient condition
guaranteeing the Input-to-State (ISS) stability property of this class of
systems is provided. The ISS property entails the boundedness of the output
reachable set of the LSTM. In light of this result, a novel approach for the
safety verification of the network, based on the Scenario Approach, is devised.
The proposed method is eventually tested on a pH neutralization process.Comment: Accepted for Learning for dynamics & control (L4DC) 202
Safety Verification for Neural Networks Based on Set-boundary Analysis
Neural networks (NNs) are increasingly applied in safety-critical systems
such as autonomous vehicles. However, they are fragile and are often
ill-behaved. Consequently, their behaviors should undergo rigorous guarantees
before deployment in practice. In this paper we propose a set-boundary
reachability method to investigate the safety verification problem of NNs from
a topological perspective. Given an NN with an input set and a safe set, the
safety verification problem is to determine whether all outputs of the NN
resulting from the input set fall within the safe set. In our method, the
homeomorphism property of NNs is mainly exploited, which establishes a
relationship mapping boundaries to boundaries. The exploitation of this
property facilitates reachability computations via extracting subsets of the
input set rather than the entire input set, thus controlling the wrapping
effect in reachability analysis and facilitating the reduction of computation
burdens for safety verification. The homeomorphism property exists in some
widely used NNs such as invertible NNs. Notable representations are invertible
residual networks (i-ResNets) and Neural ordinary differential equations
(Neural ODEs). For these NNs, our set-boundary reachability method only needs
to perform reachability analysis on the boundary of the input set. For NNs
which do not feature this property with respect to the input set, we explore
subsets of the input set for establishing the local homeomorphism property, and
then abandon these subsets for reachability computations. Finally, some
examples demonstrate the performance of the proposed method.Comment: 19 pages, 7 figure
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