Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning |
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Authors: | Shinya Kuroda Kenji Yamamoto Hiroyuki Miyamoto Kenji Doya Mitsuo Kawato |
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Institution: | (1) Kawato Dynamic Brain Project, ERATO, Japan Science and Technology Corporation, 2-2, Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan, JP;(2) Division of Signal Transduction, Nara Institute of Science and Technology, Ikoma 630-0101, Japan, JP;(3) ATR, Human Information Processing Research Laboratories, 2-2, Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan, JP;(4) Information Science Division, ATR international and CREST, Japan Science and Technology Corporation, 2-2, Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan, JP |
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Abstract: | Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain
theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs),
which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is
not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements
can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an
eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into
cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown
to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar
synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR.
To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval
probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution,
(3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a
spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual
velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models,
such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved
only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike-occurrence time after
stimulus onset must capture at least the first, second and third moments of the temporal distribution of error signals.
Received: 28 January 2000 / Accepted in revised form: 2 August 2000 |
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