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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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A graphical illustration of the plastic changes implied by the learning rules.The graphs show the spike timings and, for one synapse, the dynamics of the synaptic current , the normalized PSP  and the synaptic changes  implied by the two learning rules. It is considered that one input spike arrives at this synapse at . The synaptic changes are shown to be localized temporally along the events that cause them; the actual application of the synaptic changes can be delayed with respect to these events. (A) One independent target spike and no actual spike. (B) A pair of matching target and actual spikes, the actual one following the target one. (C) One independent actual spike and no target spike. (D) A pair of matching target and actual spikes, the target one following the actual one.
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pone-0040233-g005: A graphical illustration of the plastic changes implied by the learning rules.The graphs show the spike timings and, for one synapse, the dynamics of the synaptic current , the normalized PSP and the synaptic changes implied by the two learning rules. It is considered that one input spike arrives at this synapse at . The synaptic changes are shown to be localized temporally along the events that cause them; the actual application of the synaptic changes can be delayed with respect to these events. (A) One independent target spike and no actual spike. (B) A pair of matching target and actual spikes, the actual one following the target one. (C) One independent actual spike and no target spike. (D) A pair of matching target and actual spikes, the target one following the actual one.

Mentions: E-learning works by modifying each synaptic efficacy by terms that depend on the normalized PSP . For all target spikes that the neuron should fire, for which a spike should be created, each synaptic efficacy should be increased with a term proportional to at the moments of these target spikes. For all output spikes that should be eliminated, each synaptic efficacy needs to be decreased with a term proportional to the value of at the moments of these spikes. For all actual spikes that are close to their target positions and should be moved towards them, each synaptic efficacy needs to change with a term proportional to the value of at the moments of the actual spikes, multiplied by the temporal difference between actual and target spikes. Fig. 5 illustrates the learning rule.


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

Florian RV - PLoS ONE (2012)

A graphical illustration of the plastic changes implied by the learning rules.The graphs show the spike timings and, for one synapse, the dynamics of the synaptic current , the normalized PSP  and the synaptic changes  implied by the two learning rules. It is considered that one input spike arrives at this synapse at . The synaptic changes are shown to be localized temporally along the events that cause them; the actual application of the synaptic changes can be delayed with respect to these events. (A) One independent target spike and no actual spike. (B) A pair of matching target and actual spikes, the actual one following the target one. (C) One independent actual spike and no target spike. (D) A pair of matching target and actual spikes, the target one following the actual one.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3412872&req=5

pone-0040233-g005: A graphical illustration of the plastic changes implied by the learning rules.The graphs show the spike timings and, for one synapse, the dynamics of the synaptic current , the normalized PSP and the synaptic changes implied by the two learning rules. It is considered that one input spike arrives at this synapse at . The synaptic changes are shown to be localized temporally along the events that cause them; the actual application of the synaptic changes can be delayed with respect to these events. (A) One independent target spike and no actual spike. (B) A pair of matching target and actual spikes, the actual one following the target one. (C) One independent actual spike and no target spike. (D) A pair of matching target and actual spikes, the target one following the actual one.
Mentions: E-learning works by modifying each synaptic efficacy by terms that depend on the normalized PSP . For all target spikes that the neuron should fire, for which a spike should be created, each synaptic efficacy should be increased with a term proportional to at the moments of these target spikes. For all output spikes that should be eliminated, each synaptic efficacy needs to be decreased with a term proportional to the value of at the moments of these spikes. For all actual spikes that are close to their target positions and should be moved towards them, each synaptic efficacy needs to change with a term proportional to the value of at the moments of the actual spikes, multiplied by the temporal difference between actual and target spikes. Fig. 5 illustrates the learning rule.

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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