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Train robust networks and verify network robustness

Deep learning verification is a set of techniques for assessing the properties of deep neural networks. For example, you can verify the robustness properties of a network, compute network output bounds, find adversarial examples, detect out-of-distribution data, and verify compliance with industry standards.

The Deep Learning Toolbox Verification Library support package enables testing robustness properties of deep learning networks.

  • Use the verifyNetworkRobustness function to verify network robustness to adversarial examples. A network is robust to adversarial inputs if the predicted class of the network does not change when the input is perturbed between specified lower and upper input bounds. For a set of input bounds, the function checks if the network is robust to adversarial examples between those input bounds and returns either verified, violated, or unproven.

  • Use the estimateNetworkOutputBounds function to estimate the range of output values that the network returns when the input is between specified lower and upper bounds. Use this function to estimate how sensitive the network predictions are to input perturbation.

  • Use the networkDistributionDiscriminator function to create a distribution discriminator that separates data into in- and out-of-distribution.


estimateNetworkOutputBounds Estimate output bounds of deep learning network (Since R2022b)
verifyNetworkRobustnessVerify adversarial robustness of deep learning network (Since R2022b)
networkDistributionDiscriminator Deep learning distribution discriminator (Since R2023a)
isInNetworkDistributionDetermine whether data is within the distribution of the network (Since R2023a)
distributionScoresDistribution confidence scores (Since R2023a)
driseExplain object detection network predictions using D-RISE (Since R2024a)


BaselineDistributionDiscriminatorBaseline distribution discriminator (Since R2023a)
EnergyDistributionDiscriminatorEnergy distribution discriminator (Since R2023a)
ODINDistributionDiscriminatorODIN distribution discriminator (Since R2023a)
HBOSDistributionDiscriminatorHBOS distribution discriminator (Since R2023a)