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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 timing of the output spike and on the initial state of the membrane potential.The neuron had to learn to have the same output for all inputs. The output was one spike at a given timing . At the beginning of each trial, the membrane potential  was either set to , as in the other experiments (stable initial state), or was generated randomly, with a uniform distribution, between 0 and  (random initial state). (A) The maximum load (the capacity ) as a function of the timing of the output spike . (B) The number of learning epochs required for correct learning as a function of the timing of the output spike , for various loads . (C) , as a reference for comparing the effect on learning of the initial conditions, as a function of the timing of the output spike . For this setup, the capacity and the learning time for reaching the correct output, for stable initial state, does not depend on  if it is larger than about 40 ms. Because of the exponential decay of the membrane potential of the chronotron with a time constant , the effect of the random initial state of the membrane potential on the chronotron's performance, as a function of the output spike timing , becomes insignificant at about , similarly to , as .
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pone-0040233-g014: The dependence of chronotron performance on the timing of the output spike and on the initial state of the membrane potential.The neuron had to learn to have the same output for all inputs. The output was one spike at a given timing . At the beginning of each trial, the membrane potential was either set to , as in the other experiments (stable initial state), or was generated randomly, with a uniform distribution, between 0 and (random initial state). (A) The maximum load (the capacity ) as a function of the timing of the output spike . (B) The number of learning epochs required for correct learning as a function of the timing of the output spike , for various loads . (C) , as a reference for comparing the effect on learning of the initial conditions, as a function of the timing of the output spike . For this setup, the capacity and the learning time for reaching the correct output, for stable initial state, does not depend on if it is larger than about 40 ms. Because of the exponential decay of the membrane potential of the chronotron with a time constant , the effect of the random initial state of the membrane potential on the chronotron's performance, as a function of the output spike timing , becomes insignificant at about , similarly to , as .

Mentions: Chronotron's efficacy was not affected by the initial state of their membrane potential at the beginning of trials if target spike times were set at a delay relative to the beginning of the trial of more than about 4 times the time constant of the membrane potential's exponential decay (Fig. 14).


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

Florian RV - PLoS ONE (2012)

The dependence of chronotron performance on the timing of the output spike and on the initial state of the membrane potential.The neuron had to learn to have the same output for all inputs. The output was one spike at a given timing . At the beginning of each trial, the membrane potential  was either set to , as in the other experiments (stable initial state), or was generated randomly, with a uniform distribution, between 0 and  (random initial state). (A) The maximum load (the capacity ) as a function of the timing of the output spike . (B) The number of learning epochs required for correct learning as a function of the timing of the output spike , for various loads . (C) , as a reference for comparing the effect on learning of the initial conditions, as a function of the timing of the output spike . For this setup, the capacity and the learning time for reaching the correct output, for stable initial state, does not depend on  if it is larger than about 40 ms. Because of the exponential decay of the membrane potential of the chronotron with a time constant , the effect of the random initial state of the membrane potential on the chronotron's performance, as a function of the output spike timing , becomes insignificant at about , similarly to , as .
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3412872&req=5

pone-0040233-g014: The dependence of chronotron performance on the timing of the output spike and on the initial state of the membrane potential.The neuron had to learn to have the same output for all inputs. The output was one spike at a given timing . At the beginning of each trial, the membrane potential was either set to , as in the other experiments (stable initial state), or was generated randomly, with a uniform distribution, between 0 and (random initial state). (A) The maximum load (the capacity ) as a function of the timing of the output spike . (B) The number of learning epochs required for correct learning as a function of the timing of the output spike , for various loads . (C) , as a reference for comparing the effect on learning of the initial conditions, as a function of the timing of the output spike . For this setup, the capacity and the learning time for reaching the correct output, for stable initial state, does not depend on if it is larger than about 40 ms. Because of the exponential decay of the membrane potential of the chronotron with a time constant , the effect of the random initial state of the membrane potential on the chronotron's performance, as a function of the output spike timing , becomes insignificant at about , similarly to , as .
Mentions: Chronotron's efficacy was not affected by the initial state of their membrane potential at the beginning of trials if target spike times were set at a delay relative to the beginning of the trial of more than about 4 times the time constant of the membrane potential's exponential decay (Fig. 14).

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