reachability analysis

**Reachability Analysis** for neural networks is the **computation of the set of all possible outputs (reachable set) that a network can produce given a set of allowed inputs** — determining whether any output in the reachable set violates safety specifications. **How Reachability Analysis Works** - **Input Set**: Define the input region (hyperrectangle, polytope, or $L_p$ ball). - **Layer-by-Layer**: Propagate the input set through each layer, computing the output set at each stage. - **Over-Approximation**: Use abstract domains (zonotopes, star sets, polytopes) to efficiently approximate the reachable set. - **Safety Check**: Intersect the reachable set with the unsafe region — empty intersection = safe. **Why It Matters** - **Safety Verification**: Directly answers "can this network ever produce a dangerous output?" - **Control Systems**: Essential for neural network controllers in CPS (cyber-physical systems) like equipment control. - **Full Picture**: Reachability provides the complete output range, not just worst-case bounds on a single output. **Reachability Analysis** is **mapping all possible outputs** — computing the full set of outputs a network can produce to verify no unsafe output is reachable.