Establishing low-error and fast detection methods for qubit readout is crucial for efficient quantum error correction. Here, we test neural networks to classify a collection of single-shot spin detection events, which are the readout signal of our qubit measurements. This readout signal contains a stochastic peak, for which a Bayesian inference filter including Gaussian noise is theoretically optimal. Hence, we benchmark our neural networks trained by various strategies versus this latter algorithm. Training of the network with 106 experimentally recorded single-shot readout traces does not improve the post-processing performance. A network trained by synthetically generated measurement traces performs similar in terms of the detection error and the post-processing speed compared to the Bayesian inference filter. This neural network turns out to be more robust to fluctuations in the signal offset, length and delay as well as in the signal-to-noise ratio. Notably, we find an increase of 7% in the visibility of the Rabi oscillation when we employ a network trained by synthetic readout traces combined with measured signal noise of our setup. Our contribution thus represents an example of the beneficial role which software and hardware implementation of neural networks may play in scalable spin qubit processor architectures.