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gru.py
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import torch
import torch.nn as nn
import numpy as np
import itertools
class Sigmoid:
"""docstring for Sigmoid"""
def __init__(self):
pass
def forward(self, x):
self.res = 1/(1+np.exp(-x))
return self.res
def backward(self):
return self.res * (1-self.res)
def __call__(self, x):
return self.forward(x)
class Tanh:
def __init__(self):
pass
def forward(self, x):
self.res = np.tanh(x)
return self.res
def backward(self):
return 1 - (self.res**2)
def __call__(self, x):
return self.forward(x)
class GRU_Cell:
"""docstring for GRU_Cell"""
def __init__(self, in_dim, hidden_dim):
self.d = in_dim
self.h = hidden_dim
h = self.h
d = self.d
self.Wzh = np.random.randn(h,h)
self.Wrh = np.random.randn(h,h)
self.Wh = np.random.randn(h,h)
self.Wzx = np.random.randn(h,d)
self.Wrx = np.random.randn(h,d)
self.Wx = np.random.randn(h,d)
self.dWzh = np.zeros((h,h))
self.dWrh = np.zeros((h,h))
self.dWh = np.zeros((h,h))
self.dWzx = np.zeros((h,d))
self.dWrx = np.zeros((h,d))
self.dWx = np.zeros((h,d))
self.z_act = Sigmoid()
self.r_act = Sigmoid()
self.h_act = Tanh()
def forward(self, x, h):
# input:
# - x: shape(input dim), observation at current time-step
# - h: shape(hidden dim), hidden-state at previous time-step n
#
# output:
# - h_t: hidden state at current time-step
# reset gate
# r = self.r_act(np.matmul(self.Wrh, h) + np.matmul(self.Wrx, x))
# # input gate
# z = self.z_act(np.matmul(self.Wzh, h) + np.matmul(self.Wzx, x))
# # update gate
# g = self.h_act(np.matmul(self.Wh , (r * h)) + np.matmul(self.Wx, x))
# # output gate
# return (1 - z) * h + z * g
self.x = x
self.htminus1 = h
self.rt = self.r_act(self.Wrh @ self.htminus1 + self.Wrx @ self.x)
self.zt = self.z_act(self.Wzh @ self.htminus1 + self.Wzx @ self.x)
self.htilde = self.h_act(self.Wh @ (self.rt * self.htminus1) + self.Wx @ self.x)
self.h = (1 - self.zt) * self.htminus1 + self.zt * self.htilde
return self.h
def backward(self, delta):
# input:
# - delta: shape(hidden dim), summation of derivative wrt loss from next layer at
# same time-step and derivative wrt loss from same layer at
# next time-step
#
# output:
# - dx: Derivative of loss wrt the input x
# - dh: Derivative of loss wrt the input hidden h
# dLoss_dX
dHt_dHtilde = delta * self.zt
dHtilde_dX = self.h_act.backward()
dHt_dZt = delta * (self.htilde - self.htminus1)
dZt_dX = np.reshape(self.z_act.backward(), (1, self.h.size))
dHtilde_dRt = np.reshape(self.h_act.backward(), (1, self.h.size))
dRt_dX = np.reshape(self.r_act.backward(), (1, self.h.size))
dLoss_dX = ((dHt_dHtilde * dHtilde_dX) @ self.Wx) + ((dHt_dZt * dZt_dX) @ self.Wzx) + ((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * self.htminus1 * dRt_dX @ self.Wrx
# dLoss_dHtminus
dHt_dHtminus1 = (1 - self.zt) * delta
# dLoss_dHtminus1 = dHt_dHtminus1 + dHt_dHtilde * dHtilde_dHtminus1 @ self.Wh + dHt_dZt * dZt_dHtminus1 @ self.Wzh + ((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * dRt_dHtminus1 @ self.Wrh
dLoss_dHtminus1 = ((dHt_dZt * dZt_dX) @ self.Wzh) + (((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * self.htminus1 * dRt_dX @ self.Wrh) + dHt_dHtminus1 + (((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * self.rt)
# weights
dZt_dWzh = self.z_act.backward()
dRt_dWrh = self.r_act.backward()
dHtilde_dWh = self.h_act.backward()
dRt_dWrx = self.r_act.backward()
dZt_dWzx = self.z_act.backward()
dHtilde_dWx = self.h_act.backward()
# self.dWzh = (dHt_dZt * dZt_dWzh) @ self.htminus1
self.dWzh = np.reshape((dHt_dZt * dZt_dWzh), (self.h.size, 1)) @ np.reshape(self.htminus1, (1, self.h.size))
# self.dWrh = ((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * self.htminus1 * dRt_dWrh @ self.htminus1
self.dWrh = (np.reshape(((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * self.htminus1 * dRt_dWrh, (self.h.size, 1)) @ np.reshape(self.htminus1, (1, self.h.size)))
# self.dWh = dHt_dHtilde @ self.htminus1
self.dWh = np.reshape(dHt_dHtilde * dHtilde_dWh, (self.h.size, 1)) @ np.reshape(self.rt * self.htminus1, (1, self.h.size))
# self.dWzx = ((dHt_dZt * dZt_dWzx) @ self.x)
self.dWzx = np.reshape(dHt_dZt * dZt_dWzx, (self.h.size, 1)) @ np.reshape(self.x, (1, self.x.size))
# self.dWrx = ((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * self.htminus1 * dRt_dWrx @ self.x
self.dWrx = np.reshape(((dHt_dHtilde * dHtilde_dRt) @ self.Wh) * self.htminus1 * dRt_dWrx, (self.h.size, 1)) @ np.reshape(self.x, (1, self.x.size))
# self.dWx = (dHt_dHtilde * dHtilde_dWx) @ self.x
self.dWx = np.reshape((dHt_dHtilde * dHtilde_dWx), (self.h.size, 1)) @ np.reshape(self.x, (1, self.x.size))
return dLoss_dX, dLoss_dHtminus1
def test():
gru = GRU_Cell(3, 4)
x = np.array([2, 4, 6])
h = np.array([3, 5, 7, 9])
gru.forward(x, h)
delta = np.array([[0.52057634, -1.14434139, 1, 1]])
gru.backward(delta)
if __name__ == '__main__':
test()