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The chronotron: a neuron that learns to fire temporally precise spike patterns.

Florian RV - PLoS ONE (2012)

Bottom Line: When the input is noisy, the classification also leads to noise reduction.The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation.Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.

View Article: PubMed Central - PubMed

Affiliation: Center for Cognitive and Neural Studies, Romanian Institute of Science and Technology, Cluj-Napoca, Romania. florian@rist.ro

ABSTRACT
In many cases, neurons process information carried by the precise timings of spikes. Here we show how neurons can learn to generate specific temporally precise output spikes in response to input patterns of spikes having precise timings, thus processing and memorizing information that is entirely temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that provides high memory capacity (E-learning), and one that has a higher biological plausibility (I-learning). With I-learning, the neuron learns to fire the target spike trains through synaptic changes that are proportional to the synaptic currents at the timings of real and target output spikes. We study these learning rules in computer simulations where we train integrate-and-fire neurons. Both learning rules allow neurons to fire at the desired timings, with sub-millisecond precision. We show how chronotrons can learn to classify their inputs, by firing identical, temporally precise spike trains for different inputs belonging to the same class. When the input is noisy, the classification also leads to noise reduction. We compute lower bounds for the memory capacity of chronotrons and explore the influence of various parameters on chronotrons' performance. The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation. Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.

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The dependence of chronotron performance on the probability that input synapses receive no spikes. At the beginning of the experiment, each input spike train was set up as either one spike generated at a random timing or, with a probability , of no spikes. Input patterns did not change during learning. (A) The maximum load (the capacity ) as a function of the no firing probability . (B) The number of learning epochs required for correct learning as a function of the no firing probability , for various loads . (C) The number of learning epochs required for correct learning as a function of load , for various values of the no firing probability . Best capacity was achieved for values of  less or equal to 0.1, while fastest learning was achieved when there was no input with no spikes. For large  there are not enough input spikes to drive the neuron and, as expected, performance drops.
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pone-0040233-g013: The dependence of chronotron performance on the probability that input synapses receive no spikes. At the beginning of the experiment, each input spike train was set up as either one spike generated at a random timing or, with a probability , of no spikes. Input patterns did not change during learning. (A) The maximum load (the capacity ) as a function of the no firing probability . (B) The number of learning epochs required for correct learning as a function of the no firing probability , for various loads . (C) The number of learning epochs required for correct learning as a function of load , for various values of the no firing probability . Best capacity was achieved for values of less or equal to 0.1, while fastest learning was achieved when there was no input with no spikes. For large there are not enough input spikes to drive the neuron and, as expected, performance drops.

Mentions: In our setups, information was represented in the precise timings of spikes relative to the beginning of trials of constant duration. If trials correspond to periods of a background oscillation, the timing of spikes corresponds to the phase relative to this oscillation. Simulations performed in this framework have shown that chronotrons have the best efficacy when both input and output spike trains consist of one spike per trial (period). Setups where inputs or outputs consisted of more than one spike, or where some of the inputs fired no spikes, had suboptimal performance in terms of learning speed and memory capacity (Figs. 11, 12, and 13). However, learning was still possible under all of these conditions, unless the input pattern included too few spikes (less than about 100, for our setup).


The chronotron: a neuron that learns to fire temporally precise spike patterns.

Florian RV - PLoS ONE (2012)

The dependence of chronotron performance on the probability that input synapses receive no spikes. At the beginning of the experiment, each input spike train was set up as either one spike generated at a random timing or, with a probability , of no spikes. Input patterns did not change during learning. (A) The maximum load (the capacity ) as a function of the no firing probability . (B) The number of learning epochs required for correct learning as a function of the no firing probability , for various loads . (C) The number of learning epochs required for correct learning as a function of load , for various values of the no firing probability . Best capacity was achieved for values of  less or equal to 0.1, while fastest learning was achieved when there was no input with no spikes. For large  there are not enough input spikes to drive the neuron and, as expected, performance drops.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3412872&req=5

pone-0040233-g013: The dependence of chronotron performance on the probability that input synapses receive no spikes. At the beginning of the experiment, each input spike train was set up as either one spike generated at a random timing or, with a probability , of no spikes. Input patterns did not change during learning. (A) The maximum load (the capacity ) as a function of the no firing probability . (B) The number of learning epochs required for correct learning as a function of the no firing probability , for various loads . (C) The number of learning epochs required for correct learning as a function of load , for various values of the no firing probability . Best capacity was achieved for values of less or equal to 0.1, while fastest learning was achieved when there was no input with no spikes. For large there are not enough input spikes to drive the neuron and, as expected, performance drops.
Mentions: In our setups, information was represented in the precise timings of spikes relative to the beginning of trials of constant duration. If trials correspond to periods of a background oscillation, the timing of spikes corresponds to the phase relative to this oscillation. Simulations performed in this framework have shown that chronotrons have the best efficacy when both input and output spike trains consist of one spike per trial (period). Setups where inputs or outputs consisted of more than one spike, or where some of the inputs fired no spikes, had suboptimal performance in terms of learning speed and memory capacity (Figs. 11, 12, and 13). However, learning was still possible under all of these conditions, unless the input pattern included too few spikes (less than about 100, for our setup).

Bottom Line: When the input is noisy, the classification also leads to noise reduction.The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation.Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.

View Article: PubMed Central - PubMed

Affiliation: Center for Cognitive and Neural Studies, Romanian Institute of Science and Technology, Cluj-Napoca, Romania. florian@rist.ro

ABSTRACT
In many cases, neurons process information carried by the precise timings of spikes. Here we show how neurons can learn to generate specific temporally precise output spikes in response to input patterns of spikes having precise timings, thus processing and memorizing information that is entirely temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that provides high memory capacity (E-learning), and one that has a higher biological plausibility (I-learning). With I-learning, the neuron learns to fire the target spike trains through synaptic changes that are proportional to the synaptic currents at the timings of real and target output spikes. We study these learning rules in computer simulations where we train integrate-and-fire neurons. Both learning rules allow neurons to fire at the desired timings, with sub-millisecond precision. We show how chronotrons can learn to classify their inputs, by firing identical, temporally precise spike trains for different inputs belonging to the same class. When the input is noisy, the classification also leads to noise reduction. We compute lower bounds for the memory capacity of chronotrons and explore the influence of various parameters on chronotrons' performance. The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation. Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.

Show MeSH
Related in: MedlinePlus