The paper presents a supervised learning rule for a particular task where an output spiking neuron either fires one spike or does not fire, when presented with an input spike train. The analytical derivation and the simulations are sound, but the claims of biological plausibility and relevance are exaggerated.
The tempotron uses as inputs spike trains where information is encoded in the timing of spikes - either through the latency of firing or through the synchronization of firing. However, the tempotron does not control the timing of its output spike, and this timing does not carry any information. Only the presence or absence of the output spike during the duration T of the trial encodes information (one bit). Thus, the main problem of the tempotron setup is that the output of a tempotron cannot be an information-carrying input for another tempotron. This implies that a layer of tempotrons cannot meaningfully fed its output to another layer of tempotrons. Assuming, hypothetically, that there are tempotron-like neurons in the brain, they would only work in layers that are the boundary between networks with different types of information coding.
The paper assumes that after the neuron emits a spike in response to a input pattern all other incoming spikes have no effect on the neuron (are shunted), for the entire remaining duration of the trial (of the order of T=500 ms), which is artificial.
The tempotron requires information that is nonlocal in time, needing to monitor the maximum of the postsynaptic potential, and information that is not available to the neuron, such as the maximum of the postsynaptic potential that would have been reached if the neuron would have not fired. These two problems are mitigated by the authors by introducing the implementation by voltage convolution, but this variant of the tempotron is just briefly discussed. Given the claims of biological plausibility in the publication, the implementation by voltage convolution should have been presented as the proper tempotron and used for all the simulations that characterize the tempotron's behavior, and the implementation by monitoring of the maximum should have been presented as a biologically non-plausible theoretical model.
The tempotron has a binary response, hence its output cannot distinguish between more than two input categories. This is a significant functional limitation of the tempotron.
All these artificial constraints and limitations undermine the claims of biological plausibility and relevance of the paper. By trying in an artificial way (but succesfully) to sell the work to Nature Neuroscience, the authors have casted a negative light over results that are fine from a theoretical or computational perspective.