Learning spatial transformations through STDP (Davison, Frégnac 2006)

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A common problem in tasks involving the integration of spatial information from multiple senses, or in sensorimotor coordination, is that different modalities represent space in different frames of reference. Coordinate transformations between different reference frames are therefore required. One way to achieve this relies on the encoding of spatial information using population codes. The set of network responses to stimuli in different locations (tuning curves) constitute a basis set of functions which can be combined linearly through weighted synaptic connections in order to approximate non-linear transformations of the input variables. The question then arises how the appropriate synaptic connectivity is obtained. This model shows that a network of spiking neurons can learn the coordinate transformation from one frame of reference to another, with connectivity that develops continuously in an unsupervised manner, based only on the correlations available in the environment, and with a biologically-realistic plasticity mechanism (spike timing-dependent plasticity).
1 . Davison AP, Fr├ęgnac Y (2006) Learning cross-modal spatial transformations through spike timing-dependent plasticity. J Neurosci 26:5604-15 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Generic;
Cell Type(s):
Gap Junctions:
Receptor(s): GabaA; AMPA;
Simulation Environment: NEURON;
Model Concept(s): Synaptic Plasticity; Long-term Synaptic Plasticity; Unsupervised Learning; STDP;
Implementer(s): Davison, Andrew [Andrew.Davison at iaf.cnrs-gif.fr];
Search NeuronDB for information about:  GabaA; AMPA;
// Template for ObjectArray class.
// This class encapsulates an n-dimensional
// array of Objects as an Object itself, so
// that it can be passed as the argument of a
// procedure.
// Syntax:
//     objref oa, size
//     size = new Vector(3)
//     size.x[0] = 2
//     size.x[1] = 3
//     size.x[2] = 2
//     oa = new ObjectArray(size,"Vector","10")
// creates a 2 x 3 x 2 array of Vectors, each of size 10.
// The Vectors can be addressed as follows, e.g. the
// value of the third element in the Vector in the 1st row
// and 1st column of the 1st slice is:
//     oa.x[0][0][0].x[3]
// The size of the array and the type of object cannot be
// changed after creation.

// Alternative syntax for arrays with equal sizes in all dimensions
//     objref oa
//     oa new ObjectArray(4,6,"Vector","10")
// creates a 6 x 6 x 6 x 6 array of Vectors.
// First argument is number of dimensions, second argument is size of
// each dimension

begintemplate ObjectArray
  public x, set, call, tcall, dimensions, size
  objref x, this, sizes
  strdef command, itr, itrlist, foreach
  create dummy_section
  proc init() { local i
    create dummy_section
    access dummy_section

    if (numarg() == 3) {
      sizes = $o1
      m = sizes.size()
    if (numarg() == 4) {
      m = $1
      sizes = new Vector(m)
      for i = 0,m-1 {
	sizes.x[i] = $2*1.0
    sprint(command,"objref x")
    for i = 0, m-1 {
    result = execute1(command,this)
    command = ""
    itrlist = ""
    foreach = ""
    for i = 0,m-1 {
      sprint(foreach,"%s for %s = 0,%d ",foreach,itr,sizes.x[i]-1)
      sprint(command,"%s for %s = 0,%d \{ ",command,itr,sizes.x[i]-1)
    if (numarg() == 3) {
      sprint(command,"%s x%s = new %s(%s)",command,itrlist,$s2,$s3)
    if (numarg() == 4) {
      sprint(command,"%s x%s = new %s(%s)",command,itrlist,$s3,$s4)
    for i = 0,m-1 {
      sprint(command,"%s \}",command)
    result = execute1(command,this)
  func dimensions() {
    return m
  func size() {
    //if called without an argument, return the size
    // of the first dimension, otherwise, return the
    // size of the dimension with index $1.
    if (numarg() == 0) {
      return sizes.x[0]
    } else {
      return sizes.x[$1]
  proc set() {
    sprint(command,"%s { x%s.%s = %g }",foreach,itrlist,$s1,$2)
  proc call() {
    sprint(command,"%s { x%s.%s(%s) }",foreach,itrlist,$s1,$s2)
  proc tcall() {
    sprint(command,"%s { x%s.%s(%s.x%s) }",foreach,itrlist,$s1,$s2,itrlist)
endtemplate ObjectArray

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