Flexible survival prediction does not by itself ensure valid inference for covariate effects or subject-specific survival probabilities. We develop FLEXI-Haz, a semiparametric deep neural network model for right-censored data that combines an interpretable linear component in the log-hazard with a flexible function of time and adjustment covariates. This formulation permits nonproportional nuisance effects while retaining interpretable regression parameters. Under regularity conditions, we establish nuisance convergence rates that are minimax optimal up to logarithmic factors over composite Holder classes, together with root-n-consistent, asymptotically normal, and semiparametrically efficient estimation of the regression parameter. For adjustment covariates with finite support, we derive the explicit influence function for cumulative hazard and construct a cross-fitted one-step estimator yielding asymptotically valid pointwise confidence intervals for subject-specific survival. Simulations demonstrate reduced bias and improved coverage relative to a proportional hazards comparator under time-varying nuisance effects. An analysis of the Rotterdam breast cancer data illustrates the consequences of flexible adjustment for inference on treatment associations.

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