  Repeating spatiotemporal spike patterns exist and carry information. Here we
investigated how a single spiking neuron can optimally respond to one given
pattern (localist coding), or to either one of several patterns (distributed
coding, i.e. the neuron's response is ambiguous but the identity of the pattern
could be inferred from the response of multiple neurons), but not to random
inputs. To do so, we extended a theory developed in a previous paper
[Masquelier, 2017], which was limited to localist coding. More specifically, we
computed analytically the signal-to-noise ratio (SNR) of a
multi-pattern-detector neuron, using a threshold-free leaky integrate-and-fire
(LIF) neuron model with non-plastic unitary synapses and homogeneous Poisson
inputs. Surprisingly, when increasing the number of patterns, the SNR decreases
slowly, and remains acceptable for several tens of independent patterns.
  In addition, we investigated whether spike-timing-dependent plasticity (STDP)
could enable a neuron to reach the theoretical optimal SNR. To this aim, we
simulated a LIF equipped with STDP, and repeatedly exposed it to multiple input
spike patterns, embedded in equally dense Poisson spike trains. The LIF
progressively became selective to every repeating pattern with no supervision,
and stopped discharging during the Poisson spike trains. Furthermore, using
certain STDP parameters, the resulting pattern detectors were optimal. Tens of
independent patterns could be learned by a single neuron using a low adaptive
threshold, in contrast with previous studies, in which higher thresholds led to
localist coding only.
  Taken together these results suggest that coincidence detection and STDP are
powerful mechanisms, fully compatible with distributed coding. Yet we
acknowledge that our theory is limited to single neurons, and thus also applies
to feed-forward networks, but not to recurrent ones.
