The multispike tempotron (MST) is a powersul, single spiking neuron model that can solve complex supervised classification tasks. It is also internally complex, computationally expensive to evaluate, and unsuitable for neuromorphic hardware. Here we aim to understand whether it is possible to simplify the MST model while retaining its ability to learn and process information. To this end, we introduce a family of generalized neuron models (GNMs) that are a special case of the spike response model and much simpler and cheaper to simulate than the MST. We find that over a wide range of parameters, the GNM can learn at least as well as the MST does. We identify the temporal autocorrelation of the membrane potential as the most important ingredient of the GNM that enables it to classify multiple spatiotemporal patterns. We also interpret the GNM as a chemical system, thus conceptually bridging computation by neural networks with molecular information processing. We conclude the letter by proposing alternative training approaches for the GNM, including error trace learning and error backpropagation.