Optimal localist and distributed coding of spatiotemporal spike patterns through STDP and coincidence detection
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Repeating spatiotemporal spike patterns exist and carry information. Here we investigate how a single neuron can optimally signal the presence of one given pattern (localist coding), or of 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). Intuitively, we should connect the detector neuron to the neurons that fire during the patterns, or during subsections of them. Using a threshold-free leaky integrate-and-fire (LIF) neuron with time constant τ, non-plastic unitary synapses and homogeneous Poisson inputs, we derived analytically the signal-to-noise ratio (SNR) of the resulting pattern detector, even in the presence of jitter. In most cases, this SNR turned out to be optimal for relatively short τ (at most a few tens of ms). Thus long patterns are optimally detected by coincidence detectors working at a shorter timescale, although these ignore most of the patterns. When increasing the number of patterns, the SNR decreases slowly, and remains acceptable for tens of independent patterns. Next, we wondered if spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimum. We simulated a LIF equipped with STDP, and repeatedly exposed it to multiple input spike patterns. The LIF progressively became selective to every repeating pattern with no supervision, even when the patterns were embedded in Poisson activity. Furthermore, using certain STDP parameters, the resulting pattern detectors were optimal. Tens of independent patterns could be learned by a single neuron with 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, compatible with distributed coding.
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