Abstract Interpretation for Neural Networks

Abstract Interpretation for neural networks is the application of formal verification techniques from program analysis to prove properties of neural networks — over-approximating the set of possible outputs for a given set of inputs using abstract domains (intervals, zonotopes, polyhedra).

Abstract Domains for NNs

• Intervals (Boxes): Simplest domain — equivalent to IBP. Fast but loose bounds.
• Zonotopes: Affine-form abstract domain that tracks linear correlations between variables — tighter than boxes.
• DeepPoly: Combines zonotopes with back-substitution for tighter approximation.
• Polyhedra: Most precise but computationally expensive — used for small networks.

Why It Matters

• Sound: Abstract interpretation provides sound over-approximations — if the verification passes, the property truly holds.
• Scalable: Zonotope and DeepPoly domains balance precision with scalability for medium-sized networks.
• Properties: Can verify robustness, monotonicity, fairness, and other safety properties.

Abstract Interpretation is formal math for neural network properties — using abstract domains to prove that neural networks satisfy desired safety properties.