TRINITY: RESIDUAL-AWARE QUADRATIC SEEDING FOR TENSOR-TRAIN BLACK-BOX OPTIMIZATION

Trinity connects nonlinear surrogate prediction, bounded quadratic seeding and tensor-train search for discrete black-box optimization. The interface addresses branch cancellation: optimizing the quadratic branch can fail even when the full predictor is exact. For the tested DeepFM model, conditional affine corrections of its one-hidden-layer ReLU residual preserve quadratic couplings without auxiliary bits. A computable residual envelope yields a conditional retained-candidate bound, a near-sharp construction and explicit improvement conditions. Complete seeds are rescored with the full surrogate and initialize a correlated TT; only subsequent true-objective evaluations supply training labels. For the DeepFM instantiation (Trinity-D), across three photonic discretizations (512–2,048 variables), mean independently refined loss falls by 5.0%, 5.9% and 4.8% versus corrected full seeding at matched true calls and quadratic bit proposals. The ridge–DeepFM predictor reduces mean loss by 11.5% relative to Trinity-D onfresh higher-order instances, with a small regression on quadratic instances. Unequal inner work limits attribution, and classical baselines remain stronger in several settings. Recorded costs quantify conditional quantum potential without a measured quantum-speedup claim