Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions
This work addresses verification challenges for neural networks with staircase activation functions, offering incremental improvements in efficiency and accuracy.
The paper tackles neural network verification by developing a mixed-integer programming formulation with piecewise linear activation functions, reducing computational time in exact verification and improving false negative rates in inexact verifiers.
We present a technique for neural network verification using mixed-integer programming (MIP) formulations. We derive a \emph{strong formulation} for each neuron in a network using piecewise linear activation functions. Additionally, as in general, these formulations may require an exponential number of inequalities, we also derive a separation procedure that runs in super-linear time in the input dimension. We first introduce and develop our technique on the class of \emph{staircase} functions, which generalizes the ReLU, binarized, and quantized activation functions. We then use results for staircase activation functions to obtain a separation method for general piecewise linear activation functions. Empirically, using our strong formulation and separation technique, we can reduce the computational time in exact verification settings based on MIP and improve the false negative rate for inexact verifiers relying on the relaxation of the MIP formulation.