Reward modulated STDP (Legenstein et al. 2008)

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Accession:116837
"... This article provides tools for an analytic treatment of reward-modulated STDP, which allows us to predict under which conditions reward-modulated STDP will achieve a desired learning effect. These analytical results imply that neurons can learn through reward-modulated STDP to classify not only spatial but also temporal firing patterns of presynaptic neurons. They also can learn to respond to specific presynaptic firing patterns with particular spike patterns. Finally, the resulting learning theory predicts that even difficult credit-assignment problems, where it is very hard to tell which synaptic weights should be modified in order to increase the global reward for the system, can be solved in a self-organizing manner through reward-modulated STDP. This yields an explanation for a fundamental experimental result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys were rewarded for increasing the firing rate of a particular neuron in the cortex and were able to solve this extremely difficult credit assignment problem. ... In addition our model demonstrates that reward-modulated STDP can be applied to all synapses in a large recurrent neural network without endangering the stability of the network dynamics."
Reference:
1 . Legenstein R, Pecevski D, Maass W (2008) A learning theory for reward-modulated spike-timing-dependent plasticity with application to biofeedback. PLoS Comput Biol 4:e1000180 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Neocortex;
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: Python; PCSIM;
Model Concept(s): Pattern Recognition; Spatio-temporal Activity Patterns; Reinforcement Learning; STDP; Biofeedback; Reward-modulated STDP;
Implementer(s):
import os, sys
sys.path.append('../packages')
from pylab import *
from tables import *
from numpy import *
from math import *
from pypcsimplus import *
from frame import FrameAxes
import numpy

from matplotlib import rc
rc('font',**{'family':'sans-serif','sans-serif':['Computer Modern Sans serif']})
rc('text', usetex=True)
rc('font',**{'family':'sans-serif','sans-serif':['Computer Modern Sans serif']})


if len(sys.argv) > 1:
    h5filename = sys.argv[1]
else:
    h5filename = last_file(".*\.h5")
    
print " loading h5 filename : ", h5filename

h5file = openFile(h5filename, mode = "r", title = "Biofeedback DASTDP Experiment results")

p = constructParametersFromH5File(h5file)
r = constructRecordingsFromH5File(h5file)

print p


other_circ_not_ou_weights = r.other_circ_not_ou_weights.copy()
other_circ_ou_weights = r.other_circ_ou_weights.copy()

other_circ_ou_weights *= 1.0/p.WHighOUScale
other_circ_not_ou_weights *= 1.0/p.WLowOUScale


other_weights = vstack((other_circ_not_ou_weights, other_circ_ou_weights))

reinforced_circ_weights = [1,2]
r.reinforced_ou_weights = [1,2]
r.reinforced_other_weights = [1,2]

r.reinforced_ou_weights[0] = getattr(r, "reinforced_ou_weights_0")
r.reinforced_ou_weights[1] = getattr(r, "reinforced_ou_weights_1")

r.reinforced_other_weights[0] = getattr(r, "reinforced_other_weights_0")
r.reinforced_other_weights[1] = getattr(r, "reinforced_other_weights_1")

reinforced_circ_weights = [1,2]
for i in range(2):
    reinforced_circ_weights[i] = vstack((r.reinforced_ou_weights[i], r.reinforced_other_weights[i]))


reinforced_circ_weights *= 1.0/p.WLowOUScale

exc_ou_spikes = []
for i in r.exc_ou_nrn_idxs:
    exc_ou_spikes.append(r.spikes[i])
    
exc_other_spikes = []
for i in r.exc_other_nrn_idxs:
    exc_other_spikes.append(r.spikes[i])

reinforced_circ_avg_weights = [1,2]
reinforced_circ_std_weights = [1,2]

reinforced_ou_avg_weights = [1,2]
reinforced_ou_std_weights = [1,2]

reinforced_other_avg_weights = [1,2]
reinforced_other_std_weights = [1,2]


for i in range(2):
    reinforced_circ_avg_weights[i] = average(reinforced_circ_weights[i], 0)
    reinforced_circ_std_weights[i] = std(reinforced_circ_weights[i], 0)

    reinforced_ou_avg_weights[i] = average(r.reinforced_ou_weights[i], 0)
    reinforced_ou_std_weights[i] = std(r.reinforced_ou_weights[i], 0)

    reinforced_other_avg_weights[i] = average(r.reinforced_other_weights[i], 0)
    reinforced_other_std_weights[i] = std(r.reinforced_other_weights[i], 0)

other_avg_weights = average(other_weights, 0)
other_std_weights = std(other_weights, 0)


other_circ_avg_not_ou_weights = average(other_circ_not_ou_weights, 0)
other_circ_std_not_ou_weights = std(other_circ_not_ou_weights, 0)

other_circ_avg_ou_weights = average(other_circ_ou_weights, 0)
other_circ_std_ou_weights = std(other_circ_ou_weights, 0)


f = figure(1,figsize=(8,6), facecolor = 'w')

f.subplots_adjust(top= 0.93, left = 0.1, bottom = 0.10, right = 0.95, hspace = 0.76, wspace = 0.54)
clf()

# plot liquid r.spikes
nRespNeurons = 99
leftX = 20; rightX = 23 
gap_duration = 0.5

numpy.random.seed(34223515)

chosenNeuronsArray = numpy.random.permutation(p.nNeurons)[:nRespNeurons]
chosenNeuronsArraySplit1 = chosenNeuronsArray[:int(nRespNeurons / 3)]
chosenNeuronsArraySplit2 = chosenNeuronsArray[int(nRespNeurons / 3):int(2 * nRespNeurons / 3)]
chosenNeuronsArraySplit3 = chosenNeuronsArray[int(2*nRespNeurons / 3):]
chosenNeuronsArray = hstack((chosenNeuronsArraySplit1,p.reinforced_nrn_idx[0],chosenNeuronsArraySplit2,p.reinforced_nrn_idx[1],chosenNeuronsArraySplit3))

chosenSpikes = [ r.spikes[i] for i in chosenNeuronsArray ]
reinfNeuronRasterIdx = [1,2]
reinfNeuronRasterIdx[0] = int(nRespNeurons / 3)
reinfNeuronRasterIdx[1] = int(2 * nRespNeurons / 3) + 1

clipped_spikes_reinforc = [1, 2]
raster_x, raster_y = create_raster(chosenSpikes, leftX, rightX, shift = True)        
clipped_spikes_reinforc[0] = clip_window(chosenSpikes[reinfNeuronRasterIdx[0]], leftX, rightX, shift = True)
clipped_spikes_reinforc[1] = clip_window(chosenSpikes[reinfNeuronRasterIdx[1]], leftX, rightX, shift = True)

leftX_2, rightX_2 = p.Tsim/2  - 3, p.Tsim /2
raster_x_2, raster_y_2 = create_raster(chosenSpikes,leftX_2, rightX_2, shift = True)
raster_x_2 += (rightX - leftX) + gap_duration
clipped_spikes_reinforc_2 = [1,2]
clipped_spikes_reinforc_2[0] = clip_window(chosenSpikes[reinfNeuronRasterIdx[0]], leftX_2, rightX_2, shift = True) + (rightX - leftX) + gap_duration 
clipped_spikes_reinforc_2[1] = clip_window(chosenSpikes[reinfNeuronRasterIdx[1]], leftX_2, rightX_2, shift = True) + (rightX - leftX) + gap_duration


total_raster_x = hstack((raster_x, raster_x_2))
total_raster_y = hstack((raster_y, raster_y_2))

total_clip_spikes_reinforc = [1,2]

total_clip_spikes_reinforc[0] = hstack((clipped_spikes_reinforc[0], clipped_spikes_reinforc_2[0]))
total_clip_spikes_reinforc[1] = hstack((clipped_spikes_reinforc[1], clipped_spikes_reinforc_2[1]))
 
ax = subplot(2, 1, 1, projection = 'frameaxes')
plot(total_raster_x, total_raster_y, '.', color = '0.0', markersize = 0.3)
plot(total_clip_spikes_reinforc[0], [ reinfNeuronRasterIdx[0] for i in range(len(total_clip_spikes_reinforc[0])) ], '+', color = '0.0', markersize = 10, mec = 'b', mfc = 'b',  markeredgewidth = 2)
plot(total_clip_spikes_reinforc[1], [ reinfNeuronRasterIdx[1] for i in range(len(total_clip_spikes_reinforc[1])) ], '+', color = '0.0', markersize = 10, mec = 'g', mfc = 'g',  markeredgewidth = 2)

TickStep = 1.0    

xticks( hstack((arange(0, rightX - leftX + 0.01, TickStep), 
                arange(rightX -leftX + gap_duration, rightX - leftX + gap_duration + (rightX_2 - leftX_2) + 0.1, TickStep))), 
         [ "%d" % (x,) for x in arange(0, rightX - leftX + 0.01, TickStep) ] + [ "%d" % (x,) for x in arange(0, rightX_2 - leftX_2 + 0.1, TickStep) ] )
yticks([])



ylabel('100 neurons')
text(-0.09, 1.07, 'A', fontsize = 'x-large', transform = ax.transAxes )

axvline(rightX - leftX + gap_duration, color = 'k')


text(0.17, -0.33, 'time [sec]', transform = ax.transAxes )
text(0.7, -0.33, 'time [sec]', transform = ax.transAxes )



axhline(-1, 3.1/(rightX - leftX + rightX_2 - leftX_2  + gap_duration + 0.1), (2.97 + gap_duration)/(rightX - leftX + rightX_2 - leftX_2  + gap_duration + 0.1), linestyle = '-', color = (1,1,1), linewidth = 3)
xlim(0, rightX - leftX + rightX_2 - leftX_2  + gap_duration + 0.1)
    
    

ax = subplot(2, 2, 3, projection = 'frameaxes')
reinforced_nrn_rate = []
reinforced_nrn_rate.append(calc_rate_2(r.spikes[p.reinforced_nrn_idx[0]], int(p.Tsim/(p.samplingTime * p.DTsim / 4)), 40, p.Tsim))
reinforced_nrn_rate.append(calc_rate_2(r.spikes[p.reinforced_nrn_idx[1]], int(p.Tsim/(p.samplingTime * p.DTsim / 4)), 40, p.Tsim))

nrn_rate = []
for s in r.spikes[10:30]:
    nrn_rate.append(calc_rate_2(s, int(p.Tsim/(p.samplingTime * p.DTsim / 4)), 40, p.Tsim))
avg_nrn_rate = []
for i in range(len(nrn_rate[0])):
    avg_nrn_rate.append(sum([ nrn_rate[k][i] for k in range(len(nrn_rate)) ]) / len(nrn_rate))    
plot(arange(0, (len(reinforced_nrn_rate[0]) - .5) * p.DTsim * p.samplingTime / 4, p.DTsim * p.samplingTime / 4), reinforced_nrn_rate[0], 'b-', linewidth = 1.2)
plot(arange(0, (len(reinforced_nrn_rate[1]) - .5) * p.DTsim * p.samplingTime / 4, p.DTsim * p.samplingTime / 4), reinforced_nrn_rate[1], 'g-', linewidth = 1.2)
plot(arange(0, (len(avg_nrn_rate) - .5) * p.DTsim * p.samplingTime / 4, p.DTsim * p.samplingTime / 4), avg_nrn_rate, 'k--', linewidth = 1.2)
theGap = 10 * p.DTsim * p.samplingTime + 10 * p.DTsim * p.samplingTime / 4
print "theGap is", theGap
xlim(0, p.Tsim - theGap + p.Tsim/1000)
tickInterval = 300

xticks( array([ i * tickInterval - theGap for i in range(1, int(p.Tsim/tickInterval) + 1) ]), [ '%d' % (i * tickInterval / 60)  for i in range(1, int(p.Tsim/tickInterval) + 1) ])
xlabel("time [min]")
ylim(0,16.1)
yticks(arange(0,16.1,4), [ '%d' % (x,) for x in arange(0,16.1,4) ])
ylabel("rate [Hz]")
axvline(p.Tsim/2-theGap, linestyle = ':', color = 'k')    
text(-0.24, 1.15, 'B', fontsize = 'x-large', transform = ax.transAxes )


reinf_fontsize = 14
text(0.10, 1.0, 'A$\uparrow$', color = 'b', fontsize = reinf_fontsize, transform = ax.transAxes)
text(0.20, 1.01, '+', color = 'k', fontsize = reinf_fontsize - 1, transform = ax.transAxes)
text(0.28, 1.0,'B$\downarrow$', color = 'g', fontsize = reinf_fontsize, transform = ax.transAxes )

text(0.60, 1.0, 'A$\downarrow$', color = 'b', fontsize = reinf_fontsize, transform = ax.transAxes)
text(0.70, 1.01, '+', color = 'k', fontsize = reinf_fontsize - 1, transform = ax.transAxes)
text(0.78, 1.0,'B$\uparrow$', color = 'g', fontsize = reinf_fontsize, transform = ax.transAxes )



ax = subplot(2, 2, 4, projection = 'frameaxes')
plot(arange(0, (len(other_avg_weights) -0.5) * p.DTsim*p.samplingTime, p.DTsim*p.samplingTime), other_avg_weights, 'k--', linewidth = 1.2)

plot(arange(0, len(reinforced_circ_avg_weights[0])*p.DTsim*p.samplingTime, p.DTsim*p.samplingTime), reinforced_circ_avg_weights[0], 'b-', linewidth = 1.2)
plot(arange(0, len(reinforced_circ_avg_weights[1])*p.DTsim*p.samplingTime, p.DTsim*p.samplingTime), reinforced_circ_avg_weights[1], 'g-', linewidth = 1.2)

p.Wmax = 2 * p.WexcLowOU

numTicks = 10

yticks( [ i * 1.0 /numTicks * p.Wmax for i in range(numTicks+1) ], [ "%.1f" % (i * 1.0/numTicks) for i in range(numTicks+1) ] )
ylim(0.30 * p.Wmax, 0.70*p.Wmax)
axvline(p.Tsim/2, linestyle = ':' , color = 'k')            
xlim(0, p.Tsim+p.Tsim/1000)    
xticks( array([ i * tickInterval for i in range(int(p.Tsim/tickInterval) + 1) ]), [ '%d' % (i * tickInterval / 60)  for i in range(int(p.Tsim/tickInterval) + 1) ])
ylabel('avg. weights $(w/w_{max})$')

xlabel('time [min]')
text(-0.30, 1.23, 'C', fontsize = 'x-large', transform = ax.transAxes )

text(0.11, 1.0, 'A$\uparrow$', color = 'b', fontsize = reinf_fontsize, transform = ax.transAxes)
text(0.21, 1.01, '+', color = 'k', fontsize = reinf_fontsize - 1, transform = ax.transAxes)
text(0.29, 1.0,'B$\downarrow$', color = 'g', fontsize = reinf_fontsize, transform = ax.transAxes )

text(0.61, 1.0, 'A$\downarrow$', color = 'b', fontsize = reinf_fontsize, transform = ax.transAxes)
text(0.71, 1.01, '+', color = 'k', fontsize = reinf_fontsize - 1, transform = ax.transAxes)
text(0.79, 1.0,'B$\uparrow$', color = 'g', fontsize = reinf_fontsize, transform = ax.transAxes )

    
savefig("fetz_two_nrns.eps")


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