CLAD: Constrained Abstract Domain for Neural Network Verification

Hai Duong, Thanh Le, ThanhVu Nguyen

Neural network verification (NNV) formally verifies that a network satisfies a specified property for all inputs within a defined region. Modern NNV tools employ abstract domains to compute a sound over-approximation of the network's behavior from the given input region, thus the tightness of these abstractions essentially determines efficiency. A long line of increasingly precise domains has been developed, but they all describe the valid input region in the same restrictive way, e.g., an Lp-norm ball. A practical input region is rarely a simple Lp ball, but rather a combination Lp ball with additional constraints. Verifying a network over such a region with existing abstraction produces a loose over-approximation, which results in either failing to verify a property or spurious counterexamples. We introduce Constrained Lagrangian Abstract Domain (CLAD), a new abstract domain that computes a sound over-approximation of neural networks over input regions defined by a combination of convex constraints. CLAD propagates these constraints and tightens bounds over the true feasible region. However, bounding a neuron over the intersection of these constraints has no closed-form…