def backward(self, y_pred, y_train, cache):
X, h1_cache, h3_cache, score_cache, hpool_cache, hpool, nl_cache1, nl_cache3 = cache
# Output layer
grad_y = self.dloss_funs[self.loss](y_pred, y_train)
# FC-7
dh3, dW3, db3 = l.fc_backward(grad_y, score_cache)
dh3 = self.backward_nonlin(dh3, nl_cache3)
dh2, dW2, db2 = l.fc_backward(dh3, h3_cache)
dh2 = dh2.ravel().reshape(hpool.shape)
# Pool-1
dpool = l.maxpool_backward(dh2, hpool_cache)
# Conv-1
dh1 = self.backward_nonlin(dpool, nl_cache1)
dX, dW1, db1 = l.conv_backward(dh1, h1_cache)
grad = dict(
W1=dW1, W2=dW2, W3=dW3, b1=db1, b2=db2, b3=db3
)
return grad
def backward(self, train_data, y_true):
loss, self.gradients["A3"] = losses.cross_entropy_loss(self.nodes["A3"], y_true)
self.gradients["W3"], self.gradients["B3"], self.gradients["Z2"] = \
layer.fc_backward(self.gradients["A3"], self.Parameters["W3"], self.nodes["Z2"])
self.gradients["A2"] = activations.relu_backward(self.gradients["Z2"].T, self.nodes["A2"])
self.gradients["W2"], self.gradients["B2"], self.gradients["Z1"] = \
layer.fc_backward(self.gradients["A2"], self.Parameters["W2"], self.nodes["Z1"])
self.gradients["A1"] = activations.relu_backward(self.gradients["Z1"].T, self.nodes["A1"])
self.gradients["W1"], self.gradients["B1"], self.gradients["Z1"] = \
layer.fc_backward(self.gradients["A1"], self.Parameters["W1"], self.nodes["X2"])
self.gradients["Z1"] = self.gradients["Z1"].reshape((128, 16, 5, 5))
self.gradients["Maxpool2"] = layer.max_pooling_backward(self.gradients["Z1"], self.nodes["Conv2"], (2, 2))
self.gradients["K2"], self.gradients["Kb2"], self.gradients["KZ2"] = \
layer.conv_backward(self.gradients["Maxpool2"], self.Parameters["K2"], self.nodes["Maxpool1"])
self.gradients["Maxpool1"] = \
layer.max_pooling_backward(self.gradients["KZ2"], self.nodes["Conv1"], (2, 2))
self.gradients["K1"], self.gradients["Kb1"], self.gradients["KZ1"] = \
layer.conv_backward(self.gradients["Maxpool1"], self.Parameters["K1"], train_data)
return loss
def backward(self, train_data, y_true):
loss, self.gradients["A3"] = losses.cross_entropy_loss(
self.nodes["A3"], y_true)
self.gradients["W3"], self.gradients["B3"], self.gradients["Z2"] = \
layer.fc_backward(self.gradients["A3"], self.Parameters["W3"], self.nodes["Z2"])
self.gradients["A2"] = activations.relu_backward(
self.gradients["Z2"].T, self.nodes["A2"])
self.gradients["W2"], self.gradients["B2"], self.gradients["Z1"] = \
layer.fc_backward(self.gradients["A2"], self.Parameters["W2"], self.nodes["Z1"])
self.gradients["A1"] = activations.relu_backward(
self.gradients["Z1"].T, self.nodes["A1"])
self.gradients["W1"], self.gradients["B1"], self.gradients["Z1"] = \
layer.fc_backward(self.gradients["A1"], self.Parameters["W1"], train_data)
return loss
def backward(self, y_pred, y_train, d_next, cache):
X, hf, hi, ho, hc, hf_cache, hf_sigm_cache, hi_cache, hi_sigm_cache, ho_cache, ho_sigm_cache, hc_cache, hc_tanh_cache, c_old, c, c_tanh_cache, y_cache = cache
dh_next, dc_next = d_next
dy = loss_fun.dcross_entropy(y_pred, y_train)
dh, dWy, dby = l.fc_backward(dy, y_cache)
dh += dh_next
dho = c * dh
dho = l.sigmoid_backward(dho, ho_sigm_cache)
dc = ho * dh
dc = l.tanh_backward(dc, c_tanh_cache)
dc = dc + dc_next
dhf = c_old * dc
dhf = l.sigmoid_backward(dhf, hf_sigm_cache)
dhi = hc * dc
dhi = l.sigmoid_backward(dhi, hi_sigm_cache)
dhc = hi * dc
dhc = l.tanh_backward(dhc, hc_tanh_cache)
dXo, dWo, dbo = l.fc_backward(dho, ho_cache)
dXc, dWc, dbc = l.fc_backward(dhc, hc_cache)
dXi, dWi, dbi = l.fc_backward(dhi, hi_cache)
dXf, dWf, dbf = l.fc_backward(dhf, hf_cache)
dX = dXo + dXc + dXi + dXf
dh_next = dX[:, :self.H]
dc_next = hf * dc
grad = dict(Wf=dWf,
Wi=dWi,
Wc=dWc,
Wo=dWo,
Wy=dWy,
bf=dbf,
bi=dbi,
bc=dbc,
bo=dbo,
by=dby)
return grad, (dh_next, dc_next)
def backward(self, y_pred, y_train, dh_next, cache):
X, X_prime, h_old, hz, hz_cache, hz_sigm_cache, hr, hr_cache, hr_sigm_cache, hh, hh_cache, hh_tanh_cache, h, y_cache = cache
dy = loss_fun.dcross_entropy(y_pred, y_train)
dh, dWy, dby = l.fc_backward(dy, y_cache)
dh += dh_next
dhh = hz * dh
dh_old1 = (1. - hz) * dh
dhz = hh * dh - h_old * dh
dhh = l.tanh_backward(dhh, hh_tanh_cache)
dX_prime, dWh, dbh = l.fc_backward(dhh, hh_cache)
dh_prime = dX_prime[:, :self.H]
dh_old2 = hr * dh_prime
dhr = h_old * dh_prime
dhr = l.sigmoid_backward(dhr, hr_sigm_cache)
dXr, dWr, dbr = l.fc_backward(dhr, hr_cache)
dhz = l.sigmoid_backward(dhz, hz_sigm_cache)
dXz, dWz, dbz = l.fc_backward(dhz, hz_cache)
dX = dXr + dXz
dh_old3 = dX[:, :self.H]
dh_next = dh_old1 + dh_old2 + dh_old3
grad = dict(Wz=dWz,
Wr=dWr,
Wh=dWh,
Wy=dWy,
bz=dbz,
br=dbr,
bh=dbh,
by=dby)
return grad, dh_next
def backward(self, y_pred, y_train, cache):
X, h1_cache, h2_cache, score_cache, nl_cache1, nl_cache2, u1, u2, bn1_cache, bn2_cache = cache
# Output layer
grad_y = self.dloss_funs[self.loss](y_pred, y_train)
# Third layer
dh2, dW3, db3 = l.fc_backward(grad_y, score_cache)
dW3 += reg.dl2_reg(self.model['W3'], self.lam)
dh2 = self.backward_nonlin(dh2, nl_cache2)
dh2 = l.dropout_backward(dh2, u2)
dh2, dgamma2, dbeta2 = l.bn_backward(dh2, bn2_cache)
# Second layer
dh1, dW2, db2 = l.fc_backward(dh2, h2_cache)
dW2 += reg.dl2_reg(self.model['W2'], self.lam)
dh1 = self.backward_nonlin(dh1, nl_cache1)
dh1 = l.dropout_backward(dh1, u1)
dh1, dgamma1, dbeta1 = l.bn_backward(dh1, bn1_cache)
# First layer
_, dW1, db1 = l.fc_backward(dh1, h1_cache)
dW1 += reg.dl2_reg(self.model['W1'], self.lam)
grad = dict(W1=dW1,
W2=dW2,
W3=dW3,
b1=db1,
b2=db2,
b3=db3,
gamma1=dgamma1,
gamma2=dgamma2,
beta1=dbeta1,
beta2=dbeta2)
return grad
def backward(self, y_pred, y_train, dh_next, cache):
X, Whh, h, hprev, y, h_cache, y_cache = cache
# Softmax gradient
dy = loss_fun.dcross_entropy(y_pred, y_train)
# Hidden to output gradient
dh, dWhy, dby = l.fc_backward(dy, y_cache)
dh += dh_next
dby = dby.reshape((1, -1))
# tanh
dh = l.tanh_backward(dh, h_cache)
# Hidden gradient
dbh = dh
dWhh = hprev.T @ dh
dWxh = X.T @ dh
dh_next = dh @ Whh.T
grad = dict(Wxh=dWxh, Whh=dWhh, Why=dWhy, bh=dbh, by=dby)
return grad, dh_next