Probabilistic versus Incremental Presynaptic Learning in Biologically Plausible Synapses - Foundations on Natural and Artificial Computation - page 80

Probabilistic versus Incremental Presynaptic
Learning in Biologically Plausible Synapses

Francisco Javier Ropero Pelaez 1 and Diego Andina 2

1 Center for Mathematics, Computation and Cognition, Federal University of ABC
[e-mail]
2 Group for automation in signals and communication. UPM, Spain
[e-mail]

Abstract. In this paper, the presynaptic rule, a classical rule for heb-
bian learning, is revisited. It is shown that the presynaptic rule ex-
hibits relevant synaptic properties like synaptic directionality, and LTP
metaplasticity (long-term potentiation threshold metaplasticity). With
slight modifications, the presynaptic model also exhibits metaplasticity
of the long-term depression threshold, being also consistent with Artola,
Brocher and Singer's (ABS) influential model. Two asymptotically equiv-
alent versions of the presynaptic rule were adopted for this analysis: the
first one uses an incremental equation while the second, conditional prob-
abilities. Despite their simplicity, both types of presynaptic rules exhibit
sophisticated biological properties, specially the probabilistic version.

Keywords: Metaplasticity, ABS rule, NMDA channel, BCM rule.

1 Introduction

Synapses are neural structures that modulate presynaptic activity, converting
this activity into a higher or lower postsynaptic activation (voltage). The magni-
tude that relates postsynaptic voltage with presynaptic activity is called synaptic
eciency or synaptic weight.
To model brain learning, it is necessary to start with a plausible hypothe-
sis of synaptic weight modification. According to the plasticity curve in Figure
1.a, synaptic modification depends on the value “ a ” of postsynaptic activation
[1]. If the value (voltage) of this postsynaptic depolarization is above the Long-
Term Potentiation (LTP) threshold (white dot), a positive variation of synaptic
weight, that is, synaptic potentiation, occurs. If the value of postsynaptic ac-
tivation is between the LTP threshold and the Long-Term Depression (LTD)
threshold (black dot), a negative variation of synaptic weight, that is, synap-
tic depression, takes place. Below the LTD threshold, neither potentiation nor
depression occurs.
Another important property related to synaptic plasticity is metaplasticity
[2] which is a homosynaptic property. Metaplasticity is related to the change in
the shape of the plasticity curve by either a change of the regime (average over