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. 2020 Jun 13;12224:3–17. doi: 10.1007/978-3-030-53288-8_1

Table 1.

Overview of major features available in NNV. Links refer to relevant files/classes in the NNV codebase. BN refers to batch normalization layers, FC to fully-connected layers, AvgPool to average pooling layers, Conv to convolutional layers, and MaxPool to max pooling layers.

Feature Exact analysis Over-approximate analysis
Components FFNN, CNN, NNCS FFNN, CNN, NNCS
Plant dynamics (for NNCS) Linear ODE Linear ODE, Nonlinear ODE
Discrete/Continuous (for NNCS) Discrete Time Discrete Time, Continuous Time
Activation functions ReLU, Satlin ReLU, Satlin, Sigmoid, Tanh
CNN Layers MaxPool, Conv, BN, AvgPool, FC MaxPool, Conv, BN, AvgPool, FC
Reachability methods Star, Polyhedron, ImageStar Star, Zonotope, Abstract-domain, ImageStar
Reachable set/Flow-pipe Visualization Yes Yes
Parallel computing Yes Partially supported
Safety verification Yes Yes
Falsification Yes Yes
Robustness verification (for FFNN/CNN) Yes Yes
Counterexample generation Yes Yes