Deep Neural Network(DNN) verification is a process of verifying whether, for every possible input, the neural network output satisfies the desired properties. Simply put, it's checking for relations between the neural network input and ouput to see whether the specific properties between them of interest hold.
Using the notations of the above illustration, assume X is the input set (the set of all possible inputs the neural net can receive), Y the output set (the set of outputs desired), and f the function that represents the composite of all the operations that goes on in the hidden layers.
Then, the verification process is simply proving the above assertion holds.
Reference:
https://medium.com/sw-verification-testing/what-is-deep-neural-network-verification-and-why-is-it-important-75281738f5db
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