arXiv:2609.29335v2 Announce Type: replace-cross Abstract: In genomics, imaging and clinical studies, only a few of many candidate predictors are often nonlinearly associated with a response that may be, e.g. binary, categorical, a count or a censored event time. The Terminating-Random Experiments (T-Rex) selector is a scalable variable selection method that controls the false discovery rate (FDR) by letting synthetic null variables (dummies) compete with the real predictors. While the FDR control theory embraces more general settings, to date, the T-Rex selector has been specified only for linear models. We propose a memory-efficient selection procedure with FDR control for generalized linear models and Cox regression by extending the recently developed virtual dummy construction to score-based forward selection for Bernoulli, Poisson, multinomial and Cox responses. The virtual-dummy-based selection path remains equal in distribution to explicit augmentation, so FDR control carries over under the same assumptions. Simulations confirm this equivalence and the power gained by correct model specification. Real-world applicability is illustrated on simulated genotypes and on cancer survival data.