def derivative(V, W, t, I_ext, self):
M_inf = (1 / 2) * (1 + bm.tanh((V - self.V1) / self.V2))
I_Ca = self.g_Ca * M_inf * (V - self.V_Ca)
I_K = self.g_K * W * (V - self.V_K)
I_Leak = self.g_leak * (V - self.V_leak)
dVdt = (-I_Ca - I_K - I_Leak + I_ext) / self.C
tau_W = 1 / (self.phi * bm.cosh((V - self.V3) / (2 * self.V4)))
W_inf = (1 / 2) * (1 + bm.tanh((V - self.V3) / self.V4))
dWdt = (W_inf - W) / tau_W
return dVdt, dWdt
def update(self, x):
xh = bm.concatenate([x, self.h], axis=-1)
if self.b is None:
gated = xh @ self.w
else:
gated = xh @ self.w + self.b
i, g, f, o = bm.split(gated, indices_or_sections=4, axis=-1)
c = bm.sigmoid(f + 1.) * self.c + bm.sigmoid(i) * bm.tanh(g)
h = bm.sigmoid(o) * bm.tanh(c)
self.h.value = h
self.c.value = c
return self.h.value
def update(self, x):
if self.bz is None:
z = bm.sigmoid(x @ self.w_iz + self.h @ self.w_hz)
r = bm.sigmoid(x @ self.w_ir + self.h @ self.w_hr)
a = bm.tanh(x @ self.w_ia + (r * self.h) @ self.w_ha)
self.h.value = (1 - z) * self.h + z * a
return self.h.value
else:
z = bm.sigmoid(x @ self.w_iz + self.h @ self.w_hz + self.bz)
r = bm.sigmoid(x @ self.w_ir + self.h @ self.w_hr + self.br)
a = bm.tanh(x @ self.w_ia + (r * self.h) @ self.w_ha + self.ba)
self.h.value = (1 - z) * self.h + z * a
return self.h.value
def dV(self, V, t, W, Iext): M_inf = (1 / 2) * (1 + bm.tanh((V - self.V1) / self.V2)) I_Ca = self.g_Ca * M_inf * (V - self.V_Ca) I_K = self.g_K * W * (V - self.V_K) I_Leak = self.g_leak * (V - self.V_leak) dVdt = (- I_Ca - I_K - I_Leak + Iext) / self.C return dVdt
def update(self, x):
# update the hidden and output state
dhdt = -self.h + bm.dot(x, self.w_ir)
dhdt += bm.dot(self.r, self.w_rr)
dhdt += bm.dot(self.o, self.w_or)
self.h += self.dt / self.tau * dhdt
self.r.value = bm.tanh(self.h)
self.o.value = bm.dot(self.r, self.w_ro)
def __init__(self,
num_input,
num_hidden,
num_output,
tau=1.0,
dt=0.1,
g=1.8,
alpha=1.0,
**kwargs):
super(EchoStateNet, self).__init__(**kwargs)
# parameters
self.num_input = num_input
self.num_hidden = num_hidden
self.num_output = num_output
self.tau = tau
self.dt = dt
self.g = g
self.alpha = alpha
# weights
self.w_ir = bm.random.normal(size=(num_input,
num_hidden)) / bm.sqrt(num_input)
self.w_rr = g * bm.random.normal(
size=(num_hidden, num_hidden)) / bm.sqrt(num_hidden)
self.w_or = bm.random.normal(size=(num_output, num_hidden))
w_ro = bm.random.normal(size=(num_hidden,
num_output)) / bm.sqrt(num_hidden)
self.w_ro = bm.Variable(w_ro)
# variables
self.h = bm.Variable(bm.random.normal(size=num_hidden) * 0.5) # hidden
self.r = bm.Variable(bm.tanh(self.h)) # firing rate
self.o = bm.Variable(bm.dot(self.r, w_ro)) # output unit
self.P = bm.Variable(bm.eye(num_hidden) *
self.alpha) # inverse correlation matrix
def dW(self, W, t, V): tau_W = 1 / (self.phi * bm.cosh((V - self.V3) / (2 * self.V4))) W_inf = (1 / 2) * (1 + bm.tanh((V - self.V3) / self.V4)) dWdt = (W_inf - W) / tau_W return dWdt