AI-Driven Discovery of Information-Efficient Collider Observables for Interference Measurements

Optimal observables provide statistically powerful probes of small deformations from a reference theory, but in realistic collider measurements they are rarely available in compact analytic form. We show that interpretable event-level observables can be discovered by AI-driven symbolic evolution using score information from matrix-element reweighting as the statistical target. Focusing on the CP-sensitive interaction $HZ_{\mu\nu}\tilde Z^{\mu\nu}$, we study two complementary realizations of the same coupling structure: associated production $e^+e^-\to Z(\to \mu^-\mu^+)H$ and the decay channel $pp\to H\to ZZ^*\to e^-e^+\mu^-\mu^+$. The learned observables retain substantially more local Fisher information than standard angular baselines while remaining compact analytic functions. In both cases, the discovered expressions recover characteristic helicity-interference harmonics. In associated production these harmonics are supplemented by laboratory-frame asymmetry mappings, while in four-lepton decay the robust component is the angular kernel, with the mass-ratio factor serving as a bounded representative prefactor. These results recast optimal-observable design as a symbolic discovery problem and provide a transparent route to information-efficient, interpretable probes of collider interference.