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.