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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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Learning of a mapping between one input pattern and one output spike train.The trained neuron receives inputs from 500 neurons. The spike trains received from these neurons form the input pattern. Each input spike train consists of one spike within the 200 ms of a trial, generated at a random timing having an uniform distribution within the trial. The target output spike train consists of spikes at 50, 100 and 150 ms. (A) Part of the input pattern and the output spike train of the trained neuron, corresponding to this input, before learning. Only some of the 500 input spike trains are illustrated. (B) The synaptic efficacies change according to E-learning, such that the trained neuron's output reproduces the target spike train. Left: The output spike train during learning. Right: The VP distance between the actual and the target output spike train, during learning. The target output is reproduced after less than 15 epochs (presentations of the input pattern). (C) The VP distance between the actual and the target output spike train during learning, for E-learning and I-learning: averages and standard deviations over 10,000 realizations of the same experiment. Each realization uses different, random input spike trains and initial values of the synaptic efficacies.
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pone-0040233-g006: Learning of a mapping between one input pattern and one output spike train.The trained neuron receives inputs from 500 neurons. The spike trains received from these neurons form the input pattern. Each input spike train consists of one spike within the 200 ms of a trial, generated at a random timing having an uniform distribution within the trial. The target output spike train consists of spikes at 50, 100 and 150 ms. (A) Part of the input pattern and the output spike train of the trained neuron, corresponding to this input, before learning. Only some of the 500 input spike trains are illustrated. (B) The synaptic efficacies change according to E-learning, such that the trained neuron's output reproduces the target spike train. Left: The output spike train during learning. Right: The VP distance between the actual and the target output spike train, during learning. The target output is reproduced after less than 15 epochs (presentations of the input pattern). (C) The VP distance between the actual and the target output spike train during learning, for E-learning and I-learning: averages and standard deviations over 10,000 realizations of the same experiment. Each realization uses different, random input spike trains and initial values of the synaptic efficacies.

Mentions: We have studied these rules in computer simulations involving integrate-and-fire neurons. Both learning rules allow a neuron to perform temporally-accurate input-output mappings. Fig. 6 illustrates learning of a mapping between one input pattern (the spike trains coming through all input synapses) and one output spike train consisting of three spikes. The learning rules perform a descent in the landscape defined by the VP or E distance (Fig. 4).


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

Florian RV - PLoS ONE (2012)

Learning of a mapping between one input pattern and one output spike train.The trained neuron receives inputs from 500 neurons. The spike trains received from these neurons form the input pattern. Each input spike train consists of one spike within the 200 ms of a trial, generated at a random timing having an uniform distribution within the trial. The target output spike train consists of spikes at 50, 100 and 150 ms. (A) Part of the input pattern and the output spike train of the trained neuron, corresponding to this input, before learning. Only some of the 500 input spike trains are illustrated. (B) The synaptic efficacies change according to E-learning, such that the trained neuron's output reproduces the target spike train. Left: The output spike train during learning. Right: The VP distance between the actual and the target output spike train, during learning. The target output is reproduced after less than 15 epochs (presentations of the input pattern). (C) The VP distance between the actual and the target output spike train during learning, for E-learning and I-learning: averages and standard deviations over 10,000 realizations of the same experiment. Each realization uses different, random input spike trains and initial values of the synaptic efficacies.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3412872&req=5

pone-0040233-g006: Learning of a mapping between one input pattern and one output spike train.The trained neuron receives inputs from 500 neurons. The spike trains received from these neurons form the input pattern. Each input spike train consists of one spike within the 200 ms of a trial, generated at a random timing having an uniform distribution within the trial. The target output spike train consists of spikes at 50, 100 and 150 ms. (A) Part of the input pattern and the output spike train of the trained neuron, corresponding to this input, before learning. Only some of the 500 input spike trains are illustrated. (B) The synaptic efficacies change according to E-learning, such that the trained neuron's output reproduces the target spike train. Left: The output spike train during learning. Right: The VP distance between the actual and the target output spike train, during learning. The target output is reproduced after less than 15 epochs (presentations of the input pattern). (C) The VP distance between the actual and the target output spike train during learning, for E-learning and I-learning: averages and standard deviations over 10,000 realizations of the same experiment. Each realization uses different, random input spike trains and initial values of the synaptic efficacies.
Mentions: We have studied these rules in computer simulations involving integrate-and-fire neurons. Both learning rules allow a neuron to perform temporally-accurate input-output mappings. Fig. 6 illustrates learning of a mapping between one input pattern (the spike trains coming through all input synapses) and one output spike train consisting of three spikes. The learning rules perform a descent in the landscape defined by the VP or E distance (Fig. 4).

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