Many communications and sensing applications hinge on the detection of a signal in a noisy, interference-heavy environment. Signal processing theory yields techniques such as the generalized likelihood ratio test (GLRT) to perform detection when the received samples correspond to a linear observation model. Numerous practical applications exist, however, where the received signal has passed through a nonlinearity, causing significant performance degradation of the GLRT. In this work, we propose prepending the GLRT detector with a neural network classifier capable of identifying the particular nonlinear time samples in a received signal. We show that pre-processing received nonlinear signals using our trained classifier to eliminate excessively nonlinear samples (i) improves the detection performance of the GLRT on nonlinear signals and (ii) retains the theoretical guarantees provided by the GLRT on linear observation models for accurate signal detection.