Neural networks have proven to be efficient for a number of practical applications ranging from image recognition to identifying phase transitions in quantum physics models. In this paper, we investigate the application of neural networks to state classification in a single-shot quantum measurement. We use dispersive readout of a superconducting transmon circuit to demonstrate an increase in assignment fidelity for both two and three state classifications. More importantly, our method is ready for on-the-fly data processing without overhead or need for large data transfer to a hard drive. In addition, we demonstrate the capacity of neural networks to be trained against experimental imperfections, such as phase drift of a local oscillator in a heterodyne detection scheme.