The limited transmitter-to-receiver stop-band isolation of the duplexers in long term evolution and 5G frequency division duplex transceivers induces leakage signals from the transmitter(s) (Tx) into the receiver(s) (Rx). These leakage signals are the root cause of a multitude of self-interference (SI) problems in the receiver path(s) diminishing a receiver's sensitivity. This work deals with second-order intermodulation distortion, arising from the Tx leakage signal in combination with a coupling between the RF- and local oscillator-ports of the Rx IQ-mixer. We propose a novel adaptive architecture, utilizing neural networks, to cancel this type of interference. In contrast to traditional adaptive filter solutions, the proposed architecture can be used even if there is no model of the system available, making it robust against modeling noise and flexible in terms of interferences that it is able to cancel. The proposed architecture outperforms existing work based on least mean squares (LMS) algorithms and converges as fast as recursive least squares algorithms while maintaining comparably low complexity as the LMS approach.