Spectral Analysis of Input Spike Trains by Spike-Timing-Dependent Plasticity
Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron “sees” the input correlations. We thus denote this unsupervised learning scheme as ‘kernel spectral component analysis’ (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a “linear” response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP. Tuning feature extraction of sensory stimuli is an important function for synaptic plasticity models. A widely studied example is the development of orientation preference in the primary visual cortex, which can emerge using moving bars in the visual field. A crucial point is the decomposition of stimuli into basic information tokens, e.g., selecting individual bars even though they are presented in overlapping pairs (vertical and horizontal). Among classical unsupervised learning models, independent component analysis (ICA) is capable of isolating basic tokens, whereas principal component analysis (PCA) cannot. This paper focuses on spike-timing-dependent plasticity (STDP), whose functional implications for neural information processing have been intensively studied both theoretically and experimentally in the last decade. Following recent studies demonstrating that STDP can perform ICA for specific cases, we show how STDP relates to PCA or ICA, and in particular explains the conditions under which it switches between them. Here information at the neuronal level is assumed to be encoded in temporal cross-correlograms of spike trains. We find that a linear spiking neuron equipped with pairwise STDP requires additional mechanisms, such as a homeostatic regulation of its output firing, in order to separate mixed correlation sources and thus perform ICA.