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.