Abstract
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, tuning 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.
Highlights
In a neural network, either biological or artificial, two forms of coding can be used: localist or distributed
This observation raises an important question, which we tried to address in this theoretical paper: can coincidence detector neurons implement both localist and distributed codes? In this context, different stimuli correspond to different spatiotemporal input spike patterns
We extended a theory that we developed in a previous paper, but which was limited to one pattern only, i.e., localist coding (Masquelier, 2017), to the multi-pattern case
Summary
Either biological or artificial, two forms of coding can be used: localist or distributed. Results indicate that some hidden neurons respond to one object category only (Zhou et al, 2015; Nguyen et al, 2016; Olah et al, 2017), while others respond to multiple different objects (Nguyen et al, 2016; Olah et al, 2017) It appears that both localist and distributed codes can be optimal, depending on the task, the layer number, and the network parameters (number of layers, neurons, etc.). Let us come back to the brain, in which computation is presumably implemented by spiking neurons performing coincidence detection (Abeles, 1982; König et al, 1996; Brette, 2015) This observation raises an important question, which we tried to address in this theoretical paper: can coincidence detector neurons implement both localist and distributed codes? This shows that STDP and coincidence detection are compatible with distributed coding
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