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]
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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;
Spike Timing Dependent Weight Adjuster
based on Song and Abbott, 2001, but with soft weight limits
Andrew Davison, UNIC, CNRS, 2003-2005

	RANGE interval, tlast_pre, tlast_post, M, P
	RANGE deltaw, wmax, aLTP, aLTD, wprune
	GLOBAL tauLTP, tauLTD, on

	interval	(ms)	: since last spike of the other kind
	tlast_pre	(ms)	: time of last presynaptic spike
	tlast_post	(ms)	: time of last postsynaptic spike
	M			: LTD function
	P			: LTP function
	deltaw			: change in weight
	wsyn			: weight of the synapse

	interval = 0
	tlast_pre = 0
	tlast_post = 0
	M = 0
	P = 0
	deltaw = 0

	tauLTP  = 20	(ms)    : decay time for LTP part ( values from           )
	tauLTD  = 20	(ms)    : decay time for LTD part ( Song and Abbott, 2001 )
	wmax    = 1		: min and max values of synaptic weight
	aLTP    = 0.001		: amplitude of LTP steps
	aLTD    = 0.00106	: amplitude of LTD steps
	on	= 1		: allows learning to be turned on and off globally
	wprune  = 0             : default is no pruning

	if (w >= 0) {				: this is a pre-synaptic spike
		P = P*exp((tlast_pre-t)/tauLTP) + aLTP
		interval = tlast_post - t	: interval is negative
		tlast_pre = t
		deltaw = wsyn * M * exp(interval/tauLTD)
	} else {				: this is a post-synaptic spike
		M = M*exp((tlast_post-t)/tauLTD) - aLTD
		interval = t - tlast_pre	: interval is positive
		tlast_post = t
		deltaw = (wmax-wsyn) * P * exp(-interval/tauLTP)
	if (on) {
		if (wsyn > wprune) {
		  wsyn = wsyn + deltaw
		} else {
		  wsyn = 0