The number of neutrons emitted from a nuclear reaction plays a crucial role in various fields, including nuclear theory, nuclear nonproliferation, nuclear energy and nuclear criticality safety. Accurate determination of neutron multiplicities requires the application of several corrections, with dead-time correction and background subtraction being particularly significant. These corrections become more challenging for neutron detectors with time-dependent neutron capture. In this work, we perform a comprehensive study of three existing methods used for dead-time correction and background subtraction in neutron detectors with time-dependent neutron capture. The methods were tested for dead-times in the range from 0 to 1 μs using a Monte Carlo model simulating the dead-time and background effects in the standard neutron multiplicity probability distribution of 252Cf. The previous methods showed larger than desired uncertainty or systematic trade off. Those uncertainties prompted the development of a novel approach using neural networks trained with data from Monte Carlo simulations. The Neural Network method enabled the extraction of neutron multiplicity probabilities with accuracy ten times higher than the other methods with errors smaller than 1%. A similar approach using neural networks could be applied to problems where the system being studied can be accurately simulated without having an accurate analytical description available. The neural network method presented in this paper can easily be expanded if multiplicities are greater than 10.