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PLoS One
2008 Jan 02;31:e1377. doi: 10.1371/journal.pone.0001377.
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Spike timing dependent plasticity finds the start of repeating patterns in continuous spike trains.
Masquelier T
,
Guyonneau R
,
Thorpe SJ
.
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Experimental studies have observed Long Term synaptic Potentiation (LTP) when a presynaptic neuron fires shortly before a postsynaptic neuron, and Long Term Depression (LTD) when the presynaptic neuron fires shortly after, a phenomenon known as Spike Timing Dependent Plasticity (STDP). When a neuron is presented successively with discrete volleys of input spikes STDP has been shown to learn 'early spike patterns', that is to concentrate synaptic weights on afferents that consistently fire early, with the result that the postsynaptic spike latency decreases, until it reaches a minimal and stable value. Here, we show that these results still stand in a continuous regime where afferents fire continuously with a constant population rate. As such, STDP is able to solve a very difficult computational problem: to localize a repeating spatio-temporal spike pattern embedded in equally dense 'distractor' spike trains. STDP thus enables some form of temporal coding, even in the absence of an explicit time reference. Given that the mechanism exposed here is simple and cheap it is hard to believe that the brain did not evolve to use it.
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Figure 1. Spatio-temporal spike pattern.Here we show in red a repeating 50 ms long pattern that concerns 50 afferents among 100. The bottom panel plots the population-averaged firing rates over 10 ms time bins (we chose 10 ms because it is the membrane time constant of the neuron used later in the simulations), and demonstrates that nothing characterizes the periods when the pattern is present. The right panel plots the individual firing rates averaged over the whole period. Neurons involved in the pattern are shown in red. Again, nothing characterizes them in terms of firing rates. Detecting the pattern thus requires taking the spike times into account.
Figure 2. The STDP modification function.We plotted the additive weight updates as a function of the difference between the presynaptic spike time and the postsynaptic one. We used an exponential law (see Materials and Methods). The left part corresponds to Long Term Potentiation (LTP) and the right part to Long Term Depression (LTD).
Figure 3. Leaky Integrate-and-Fire (LIF) neuron.Here is an illustrative example with only 6 input spikes. The graph plots the membrane potential as a function of time, and clearly demonstrates the effects of the 6 corresponding Excitatory PostSynaptic Potentials (EPSP). Because of the leak, for the threshold to be reached the input spikes need to be nearly synchronous. The LIF neuron is thus acting as a coincidence detector. When the threshold is reached, a postsynaptic spike is fired. This is followed by a refractory period of 1 ms and a negative spike-afterpotential.
Figure 4. Overview of the 450 s simulation.Here we plotted the membrane potential as a function of simulation time, at the beginning, middle, and end of the simulation. Grey rectangles indicate pattern presentations. (a) At the beginning of the simulation the neuron is non-selective because the synaptic weights are all equal. It thus fires periodically, both inside and outside the pattern. (b) At t≈13.5 s, after about 70 pattern presentations and 700 discharges, selectivity to the pattern is emerging: gradually the neuron almost stops discharging outside the pattern (no false alarms), while it does discharge most of the time the pattern is present (high hit rate), here even twice (c) End of the simulation. The system has converged (by saturation). Postsynaptic spike latency is about 4 ms. Hit rate is 99.1% with no false alarms (estimated on the last 150 s).
Figure 5. Latency reduction.Here we plotted the postsynaptic latency as a function of the number of discharges (by convention the latency is 0 when the neuron discharged outside the pattern, i.e. when it generated a false alarm). We clearly distinguish 3 periods: the beginning, when the neuron is non-selective; the middle, when selectivity has emerged and STDP is ‘tracking back’ through the pattern; and the end, when the system has converged towards a fast and reliable pattern detector.
Figure 6. Converged state (a) we represented the spike trains of the 2,000 afferents.We have reordered the afferents with respect to Fig. 1 so that afferents 1–1000 are involved in the pattern, and afferents 1001–2000 are not and we use a color code ranging from black for spikes that correspond to completely depressed synapses (weight = 0) to white for spikes that correspond to maximally potentiated synapses (weight = 1). This allows the visualization of the spikes which generate a significant EPSP and those which do not. The pattern is represented with a grey line rectangle. Notice the cluster of white spikes at the beginning of it: STDP has potentiated most of the synapses that correspond to the earliest spikes of the pattern. Note that virtually all the synaptic connections with afferents not involved in the pattern have been completely depressed. (b) The membrane potential is plotted as a function of time, over the same range as above. We clearly see the sudden increase that corresponds to the above-mentioned cluster.
Figure 7. Resistance to degradations (100 trials).(a) Percentage of successful trials as a function of the pattern frequency (pattern duration/the total duration, given a fixed pattern length of 50 ms). The pattern needs to be consistently present, at least at the beginning, for the STDP to start the learning process. (b) Percentage of successful trials as a function of jitter. For jitter greater than 3 ms spike coincidences are lost and the STDP weight updates are inaccurate, so the learning is impaired (c) Percentage of successful trials as a function of the proportion of afferents involved in the pattern. Performance is good if this proportion is above 1/3 (d) Percentage of successful trials as a function of the initial weights. With a high value the neuron can handle more discharges outside the pattern. (e) Percentage of successful trials as a function of the proportion of spikes deleted. With a 10% deletion the pattern was correctly learnt in 82% of the cases.
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