% Network of Izhikevich Neurons learns a song bird signal with a clock
% input. Note that you have to supply your own supervisor here due to file
% size limitations. The supervisor, zx should be a matrix of m x nt dimensional, where
% m is the dimension of the supervisor and nt is the number of time steps.
% RLS is applied until time T/2. The HDTS is stored as variable z2. Note
% that the code is written for a 5 second supervisor, nt should equal the
% length of z2.
clear all
clc
T = 100000; %Network parameters and total simulation time
dt = 0.04; %Time step
nt = round(T/dt); %number of time steps
N = 1000; %number of neurons
%% Izhikevich Parameters
C = 250;
vr = -60;
b = 0;
ff = 2.5;
vpeak = 30;
vreset = -65;
vt = -40;
Er = 0;
u = zeros(N,1);
a = 0.002;
d = 100;
tr = 2;
td = 20;
p = 0.1;
G = 1.3*10^4;
Q = 1*10^3;
WE2 = 8*10^3;
%% Initialize post synaptic currents, and voltages
IPSC = zeros(N,1); %post synaptic current
h = zeros(N,1);
r = zeros(N,1);
hr = zeros(N,1);
JD = zeros(N,1);
v = vr+(vpeak-vr)*rand(N,1); %initial distribution
v_ = v; %These are just used for Euler integration, previous time step storage
%% User has to supply supervisor signal, zx
load songsup4.mat
dd = size(zx);
m1 = dd(1);
m2 = 500; %number of upstates in the supervisor signal duration of 5 seconds. 100 per second.
zx = zx/(max(max(zx)));
zx(isnan(zx)==1)=0;
%% Generate HDTS
temp1 = abs(sin(m2*pi*((1:1:5000/dt)*dt)/5000));
for qw = 1:1:m2
z2(qw,:) = temp1.*((1:1:5000/dt)*dt<qw*5000/m2).*((1:1:5000/dt)*dt>(qw-1)*5000/m2);
end
%%
dd(2) = max(size(zx));
OMEGA = G*(randn(N,N)).*(rand(N,N)<p)/(p*sqrt(N)); %Random weight matrix
z1 = zeros(m1,1);
BPhi1 = zeros(N,m1); %initialize Decoder
E1 = (2*rand(N,m1)-1)*Q; %Rank-nchord perturbation
E2 = (2*rand(N,m2)-1)*WE2; %HDTS input
tspike = zeros(8*nt,2); %spike times
ns = 0;
BIAS = 1000; %Bias, at the rheobase current.
%%
Pinv1 = eye(N)*2; %The initial correlation weight matirx
step = 100; %Total number of steps to use
imin = round(1000/dt); %First step to start RLS/FORCE method
icrit = round(0.5*T/dt); %Last step to start RLS/FORCE method
current = zeros(nt/100,m1); %Store the approxoimant
RECB = zeros(nt,10); %Store some decoders %
REC = zeros(nt,10); %Store some voltage traces
i=1; ss = 0;
qq = 1;
k2 = 0;
ns1 = 0; ns2 = 0;
%% SIMULATION
tic
ilast = i ;
%icrit = ilast;
for i = ilast:1:nt;
%% EULER INTEGRATE
I = IPSC + E1*z1 + E2*z2(:,qq) + BIAS;
v = v + dt*(( ff.*(v-vr).*(v-vt) - u + I))/C ; % v(t) = v(t-1)+dt*v'(t-1)
u = u + dt*(a*(b*(v_-vr)-u)); %same with u, the v_ term makes it so that the integration of u uses v(t-1), instead of the updated v(t)
%%
index = find(v>=vpeak);
if length(index)>0
JD = sum(OMEGA(:,index),2); %compute the increase in current due to spiking
tspike(ns+1:ns+length(index),:) = [index,0*index+dt*i]; %Store spike
%times, but takes longer to simulate.
ns = ns + length(index); %total number of spikes
end
% implement the synapse, either single or double exponential
if tr == 0
IPSC = IPSC*exp(-dt/td)+ JD*(length(index)>0)/(td);
r = r *exp(-dt/td) + (v>=vpeak)/td;
else
IPSC = IPSC*exp(-dt/tr) + h*dt;
h = h*exp(-dt/td) + JD*(length(index)>0)/(tr*td); %Integrate the current
r = r*exp(-dt/tr) + hr*dt;
hr = hr*exp(-dt/td) + (v>=vpeak)/(tr*td);
end
%Compute the approximant and error
z1 = BPhi1'*r;
if qq>=dd(2)
qq = 1;
end
err = z1 - zx(:,qq);
qq = qq + 1;
%% Implement RLS.
if mod(i,step)==1
if i > imin
if i < icrit
cd1 = Pinv1*r;
BPhi1 = BPhi1 - (cd1*err');
Pinv1 = Pinv1 -((cd1)*(cd1'))/( 1 + (r')*(cd1));
end
end
end
%Record the decoders periodically.
if mod(i,1/dt)==1
ss = ss + 1;
RECB(ss,1:10)=BPhi1(1:10);
end
% apply the resets and store stuff
u = u + d*(v>=vpeak); %implements set u to u+d if v>vpeak, component by component.
v = v+(vreset-v).*(v>=vpeak); %implements v = c if v>vpeak add 0 if false, add c-v if true, v+c-v = c
v_ = v; % sets v(t-1) = v for the next itteration of loop
REC(i,:) = [v(1:5)',u(1:5)'];
if mod(i,100) ==1 %don't store every time step, saves time.
k2 = k2 + 1;
current(k2,:) = z1';
end
%Plot progress
if mod(i,round(100/dt))==1
drawnow
%figure(1)
%plot(tspike(1:1:ns,2),tspike(1:1:ns,1),'k.')
%ylim([0,100])
gg = max(1,i-round(3000/dt));
figure(32)
plot(0.001*(1:1:k2)*dt*i/k2,current(1:1:k2,1:20:m1))
xlabel('Time')
ylabel('Network Output')
xlim([dt*i/1000-5,dt*i/1000])
ylim([0,0.4])
figure(5)
plot(0.001*dt*i*(1:1:ss)/ss,RECB(1:1:ss,1:10),'r.')
xlabel('Time (s)')
ylabel('Decoder')
end
end