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TRNN.py
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TRNN.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Nov 4 01:14:51 2022
@author: kevin
"""
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
matplotlib.rc('xtick', labelsize=40)
matplotlib.rc('ytick', labelsize=40)
# %% Tensor-RNN setting
N = 200 # number of neurons
k = 10 # temporal kernel
g = 1.5 # scaling strength
M = np.random.randn(N,N,k)*g*1/np.sqrt(N) # tensor network
# %% construct more stable network
taus = np.random.rand(N**2)
taus = taus*k # kernel time scale
amps = np.random.rand(N**2)
amps = amps*2-1 # kernel amplitude
ii = 0
temp = np.arange(k)
for i in range(N):
for j in range(N):
M[i,j,:] = M[i,j,0]*amps[ii]*np.exp(-temp/taus[ii])
def NL(x):
nl = np.tanh(x)
# nl = 1/(1+np.exp(x))
# nl = np.exp(x)
return nl
def spk(x):
p = np.random.rand(x.shape[0])
s = x*0
s[x>p] = 1
return s
W = np.random.randn(N,k) # readout kernel
# %% dynamic target
T = 500
dt = 0.1
time = np.arange(0,T,dt)
lt = len(time)
###target pattern
amp = 0.7;
freq = 1/60;
rescale = 1.2
ft = (amp/1.0)*np.sin(1.0*np.pi*freq*time*rescale) + \
(amp/2.0)*np.sin(2.0*np.pi*freq*time*rescale) + \
(amp/6.0)*np.sin(3.0*np.pi*freq*time*rescale) + \
1*(amp/3.0)*np.sin(4.0*np.pi*freq*time*rescale)
ft = ft/.7
plt.figure()
plt.plot(time,ft)
# %% FORCE learning
# initialization
learn_every = 1
alpha = 1.
wo = W*1#np.zeros((N,k))
dw = np.zeros((N,k))
xt = np.zeros((N,lt))
x0 = np.random.randn(N,k)
xt[:,:k] = x0
rt = xt*1
zt = np.zeros(lt)
P = (1.0/alpha)*np.eye(N)
# dynamics
for tt in range(k,lt):
# rt[:,tt] = NL(np.einsum('ijk,jk->i', M, xt[:,tt-k:tt])) # kernel, network, and nonlinear
# xt[:,tt] = xt[:,tt-1] + dt*(-xt[:,tt-1] + rt[:,tt])
rt[:,tt] = NL(xt[:,tt-k:tt])[:,0] #+ np.random.randn()*0.2 # kernel, network, and nonlinear
xt[:,tt] = np.einsum('ijk,jk->i', M, rt[:,tt-k:tt])
zt[tt] = np.sum(np.einsum('ik,ik->i', wo, rt[:,tt-k:tt]))
### add IRLS here~~
# learning
if np.mod(tt, learn_every) == 0:
kk = (P @ rt[:,tt])[:,None]
rPr = rt[:,tt][:,None].T @ kk
c = 1.0/(1.0 + rPr)
P = P - (kk @ kk.T) * c #projection matrix
# update the error for the linear readout
e = zt[tt] - ft[tt] # error term
# update the output weights
dw = -(e*kk*c)#[:,None]
wo = wo + dw
# update the internal weight matrix ... need to fix this for kernels!!
# M = M + np.repeat(dw,N,1).T[:,:,None]
# np.einsum('ij,jk->ijk', np.tensordot(dw,dw.T,axes=1), dw)
#np.repeat(dw,N,1).T
### ... low-rank M
plt.figure()
plt.imshow(rt, aspect='auto')
# %% testing
# %%
###############################################################################
# target pattern
def sigmoid(x):
return 1/(1+np.exp(x))
V = 10
H = 5
N = V+H
T = 1000
px = np.random.randn(V,T)
for vv in range(V):
px[vv,:] = sigmoid(np.convolve(px[vv,:],np.ones(20),'same'))
temp = np.random.rand(V,T)
X = px*0
X[px>temp] = 1
# %%
def NL_spk(x):
return np.exp(x)
def NL_r(x):
return 10/(1+np.exp(-x))
N = 30
dt = 0.1
wind = 10
xx = np.arange(wind)
tau_h = 1
h = np.flipud(-.1*np.exp(-xx/tau_h)[:,None])[:,0]
v1,v2 = np.random.randn(N,1),np.random.randn(N,1)
v1[v1>0] = 1
v1[v1<0] = -1
v2[v2>0] = 1
v2[v2<0] = -1
J = np.random.randn(N,N)/np.sqrt(N)*.1 + (v1 @ v1.T)/N*.5 + (v2 @ v2.T)/N*.5 + (v1 @ v2.T)/N*.5
x0 = np.random.rand(N)
yt = np.zeros((N,T))
xt = yt*0
xt[:,0] = x0
for tt in range(wind,T):
xt[:,tt] = yt[:,tt-wind:tt] @ h*1 + 0.*J @ NL_r(xt[:,tt-1]) + 5.*J@yt[:,tt-1]
yt[:,tt] = np.random.poisson(NL_r(xt[:,tt])*dt)
plt.figure()
plt.imshow(yt,aspect='auto')
# %%
#def neural_model(x,theta):
# current = theta.T @ x
# sig = sigmoid(current)
# hidden = sig[-H:]
# ht = hidden*0
# ht[hidden>np.random.rand(H)] = 1
# return ht
#eta = 0.1
#kappa = 1
#alpha = 1
#theta_init = np.random.randn(N,N)