def loss(self, X, y=None):
"""
Evaluate loss and gradient for the three-layer convolutional network.
"""
W1 = self.params['W1']
W2, b2 = self.params['W2'], self.params['b2']
W3, b3 = self.params['W3'], self.params['b3']
# pass pool_param to the forward pass for the max-pooling layer
pool_param = {'pool_height': 2, 'pool_width': 2, 'stride': 2}
scores = None
conv, cache1 = layers.conv_forward(X,W1)
relu1, cache2 = layers.relu_forward(conv)
maxp, cache3 = layers.max_pool_forward(relu1,pool_param)
fc1, cache4 = layers.fc_forward(maxp,W2,b2)
relu2, cache5 = layers.relu_forward(fc1)
scores, cache6 = layers.fc_forward(relu2,W3,b3)
if y is None:
return scores
loss, grads = 0, {}
loss, dscores = layers.softmax_loss(scores,y)
dx3, dW3, db3 = layers.fc_backward(dscores,cache6)
dRelu2 = layers.relu_backward(dx3,cache5)
dx2, dW2, db2 = layers.fc_backward(dRelu2,cache4)
dmaxp = layers.max_pool_backward(dx2.reshape(maxp.shape),cache3)
dRelu1 = layers.relu_backward(dmaxp,cache2)
dx,dW1 = layers.conv_backward(dRelu1,cache1)
grads = {'W1':dW1,'W2':dW2,'b2':db2,'W3':dW3,'b3':db3}
return loss, grads
def affine_relu_backward(dout, cache):
'''
backward pass for the affine-relu convenience layer
'''
fc_cache, relu_cache = cache
da = layers.relu_backward(dout, relu_cache)
dx, dw, db = layers.affine_backward(da, fc_cache)
return dx, dw, db
def test_relulayer():
x = np.random.randn(10, 10)
dout = np.random.randn(*x.shape)
dx_num = eval_numerical_gradient_array(lambda x: layers.relu_forward(x)[0], x, dout)
_, cache = layers.relu_forward(x)
dx = layers.relu_backward(dout, cache)
# The error should be around 1e-12
print 'Testing relu layers:'
print 'dx error: ', rel_error(dx_num, dx)
def test_relulayer():
x = np.random.randn(10, 10)
dout = np.random.randn(*x.shape)
dx_num = eval_numerical_gradient_array(lambda x: layers.relu_forward(x)[0],
x, dout)
_, cache = layers.relu_forward(x)
dx = layers.relu_backward(dout, cache)
# The error should be around 1e-12
print 'Testing relu layers:'
print 'dx error: ', rel_error(dx_num, dx)
def test_relu_backward(self):
# ReLU layer: backward
np.random.seed(498)
x = np.random.randn(10, 10)
dout = np.random.randn(*x.shape)
dx_num = eval_numerical_gradient_array(
lambda x: layers.relu_forward(x)[0], x, dout)
_, cache = layers.relu_forward(x)
dx = layers.relu_backward(dout, cache)
# The error should be around 3e-12
print('\nTesting relu_backward function:')
print('dx error: ', rel_error(dx_num, dx))
np.testing.assert_allclose(dx, dx_num, atol=1e-9)
def backward(self, grad_scores, cache):
grads = None
#######################################################################
# TODO: Implement the backward pass to compute gradients for all #
# learnable parameters of the model, storing them in the grads dict #
# above. The grads dict should give gradients for all parameters in #
# the dict returned by model.parameters(). #
#######################################################################
cache11, cache12, cache2 = cache
grad_out12, grad_W2, grad_b2 = fc_backward(grad_scores, cache2)
grad_out11 = relu_backward(grad_out12, cache12)
grad_X, grad_W1, grad_b1 = fc_backward(grad_out11, cache11)
grads = {
'W1': grad_W1,
'b1': grad_b1,
'W2': grad_W2,
'b2': grad_b2,
}
#######################################################################
# END OF YOUR CODE #
#######################################################################
return grads
def loss(self, X, y=None):
"""
Compute loss and gradient for a minibatch of data.
Inputs:
- X: Array of input data of shape (N, d_in)
- y: Array of labels, of shape (N,). y[i] gives the label for X[i].
Returns:
If y is None, then run a test-time forward pass of the model and return:
- scores: Array of shape (N, C) giving classification scores, where
scores[i, c] is the classification score for X[i] and class c.
If y is not None, then run a training-time forward and backward pass and
return a tuple of:
- loss: Scalar value giving the loss
- grads: Dictionary with the same keys as self.params, mapping parameter
names to gradients of the loss with respect to those parameters.
"""
W1, b1 = self.params['W1'], self.params['b1']
W3, b3 = self.params['W3'], self.params['b3']
N, d_in = X.shape
scores = None
f, cache1 = layers.fc_forward(X, W1, b1) #fc
h, cache2 = layers.relu_forward(f) #relu
scores, cache3 = layers.fc_forward(h, W3, b3) #fc
# If y is None then we are in test mode so just return scores
if y is None:
return scores
loss, grads = 0, {}
loss, dscores = layers.softmax_loss(scores, y)
dx2, dW3, db3 = layers.fc_backward(dscores, cache3)
dx1 = layers.relu_backward(dx2, cache2)
dx, dW1, db1 = layers.fc_backward(dx1, cache1)
grads = {'W1': dW1, 'b1': db1, 'W3': dW3, 'b3': db3}
return loss, grads
def affine_relu_backward(dout, cache):
fc_cache, relu_cache = cache
da = relu_backward(dout, relu_cache)
dx, dw, db = affine_backward(da, fc_cache)
return dx, dw, db
def loss(self, X, y=None):
"""
Compute loss and gradient for a minibatch of data.
Args:
- X: Input data, numpy array of shape (N, d_1, ..., d_k)
- y: Array of labels, of shape (N,). y[i] gives the label for X[i].
Returns:
If y is None, then run a test-time forward pass of the model and
return:
- scores: Array of shape (N, C) giving classification scores, where
scores[i, c] is the classification score for X[i] and class c.
If y is not None, then run a training-time forward and backward pass
and return a tuple of:
- loss: Scalar value giving the loss
- grads: Dictionary with the same keys as self.params, mapping
parameter
names to gradients of the loss with respect to those parameters.
"""
scores = None
X = X.astype(self.dtype)
linear_cache = dict()
relu_cache = dict()
dropout_cache = dict()
"""
TODO: Implement the forward pass for the fully-connected neural
network, compute the scores and store them in the scores variable.
"""
#######################################################################
# BEGIN OF YOUR CODE #
#######################################################################
VAL = X.copy()
for i in range(1, self.num_layers):
linear_cache['L{}'.format(i)] = linear_forward(
VAL, self.params['W{}'.format(i)],
self.params['b{}'.format(i)])
relu_cache['R{}'.format(i)] = relu_forward(
linear_cache['L{}'.format(i)])
if self.use_dropout:
dropout_cache['D{}'.format(i)], dropout_cache['MASK{}'.format(i)] = dropout_forward(relu_cache['R{}'.format(i)],\
self.dropout_params['p'], self.dropout_params['train'],\
self.dropout_params['seed'])
VAL = dropout_cache['D{}'.format(i)]
else:
VAL = relu_cache['R{}'.format(i)]
linear_cache['L{}'.format(self.num_layers)] = linear_forward(VAL, self.params['W{}'.format(self.num_layers)],\
self.params['b{}'.format(self.num_layers)])
scores = linear_cache['L{}'.format(self.num_layers)]
#######################################################################
# END OF YOUR CODE #
#######################################################################
# If y is None then we are in test mode so just return scores
if y is None:
return scores
loss, grads = 0, dict()
"""
TODO: Implement the backward pass for the fully-connected net. Store
the loss in the loss variable and all gradients in the grads
dictionary. Compute the loss with softmax. grads[k] has the gradients
for self.params[k]. Add L2 regularisation to the loss function.
NOTE: To ensure that your implementation matches ours and you pass the
automated tests, make sure that your L2 regularization includes a
factor of 0.5 to simplify the expression for the gradient.
"""
#######################################################################
# BEGIN OF YOUR CODE #
#######################################################################
loss, grad = softmax(scores, y)
if self.use_dropout:
VAR = dropout_cache['D{}'.format(self.num_layers - 1)]
else:
VAR = relu_cache['R{}'.format(self.num_layers - 1)]
dX, grads['W{}'.format(self.num_layers)], grads['b{}'.format(self.num_layers)] = linear_backward(grad, \
VAR, self.params['W{}'.format(self.num_layers)],self.params['b{}'.format(self.num_layers)])
grads['W{}'.format(
self.num_layers)] += self.reg * self.params['W{}'.format(
self.num_layers)]
loss += 0.5 * self.reg * np.sum(self.params['W' + str(self.num_layers)]
**2)
for inx in range(self.num_layers - 1, 0, -1):
if self.use_dropout:
dX = dropout_backward(dX, dropout_cache['MASK{}'.format(inx)],
self.dropout_params['p'])
dX = relu_backward(dX, linear_cache['L' + str(inx)])
if inx - 1 != 0:
if self.use_dropout:
pre_layer = dropout_cache['D{}'.format(inx - 1)]
else:
pre_layer = relu_cache['R{}'.format(inx - 1)]
dX, grads['W' +
str(inx)], grads['b' + str(inx)] = linear_backward(
dX, pre_layer, self.params['W{}'.format(inx)],
self.params['b{}'.format(inx)])
grads['W' + str(inx)] += self.reg * self.params['W' + str(inx)]
loss += 0.5 * self.reg * np.sum(self.params['W' + str(inx)]**2)
else:
dX, grads['W' +
str(inx)], grads['b' + str(inx)] = linear_backward(
dX, X, self.params['W{}'.format(inx)],
self.params['b{}'.format(inx)])
grads['W' + str(inx)] += self.reg * self.params['W' + str(inx)]
loss += 0.5 * self.reg * np.sum(self.params['W' + str(inx)]**2)
#######################################################################
# END OF YOUR CODE #
#######################################################################
return loss, grads
# In the file layers.py implement the backward pass for the ReLU activation in # # the relu_backward function. # # Once you are done you can test your implementation using the numeric gradient # # checking. # ################################################################################### # Test the relu_backward function x = np.random.randn(10, 10) dout = np.random.randn(*x.shape) if layers.relu_forward(x)[0] is not None: dx_num = eval_numerical_gradient_array(lambda x: layers.relu_forward(x)[0], x, dout) _, cache = layers.relu_forward(x) dx = layers.relu_backward(dout, cache) # The error should be around 1e-12 print 'Testing relu_backward function:' print 'dx error: (should be around 1e-12): ', rel_error(dx_num, dx) ################################################################################### # Sandwich layers # ################################################################################### # There are some common patterns of layers that are frequently used in # # neural nets. For example, affine layers are frequently followed by a # # ReLU nonlinearity. To make these common patterns easy, we define # # several convenience layers in the file layer_utils.py. For now # # take a look at the affine_relu_forward and affine_relu_backward # # functions, and run the following to numerically gradient check the #
def loss(self,X,y=None):
X = X.astype(self.dtype)
mode = 'test' if y is None else 'train'
if self.use_dropout :
self.dropout_param['mode'] = mode
if self.use_batchnorm:
for bn_param in self.bn_params:
bn_param['mode'] = mode
scores = None
inputi = X
batch_size = X.shape[0]
X = np.reshape(X,[batch_size,-1])
fc_cache_list = []
relu_cache_list = []
bn_cache_list = []
dropout_cache_list = []
for i in range(self.num_layers-1):
fc_act,fc_cache= affine_forward(X,self.params['W'+str(i+1)],self.params['b'+str(i+1)])
fc_cache_list.append(fc_cache)
if self.use_batchnorm:
bn_act,bn_cache = batchnorm_forward(fc_act,self.params['gamma'+str(i+1)],self.params['beta'+str(i+1)],self.bn_params[i])
bn_cache_list.append(bn_cache)
relu_act,relu_cache = relu_forward(bn_act)
relu_cache_list.append(relu_cache)
else:
relu_act,relu_cache = relu_forward(fc_act)
relu_cache_list.append(relu_cache)
if self.use_dropout:
relu_act,dropout_cache = dropout_forward(relu_act,self.dropout_param)
dropout_cache_list.append(dropout_cache)
X = relu_act.copy()
########最后一层
scores,final_cache = affine_forward(X,self.params['W'+str(self.num_layers)],self.params['b'+str(self.num_layers)])
#
# for layer in range(self.num_layers):
# Wi,bi = self.params['W%d'%(layer+1)],self.params['b%d'%(layer+1)]
# outi,fc_cachei = affine_forward(inputi,Wi,bi)
# fc_cache_list.append(fc_cachei)
#
# if self.use_batchnorm and layer!=self.num_layers-1:
# gammai,betai = self.params['gamma%d'%(layer+1)],self.params['beta%d'%(layer+1)]
#
# outi,bn_cachei = batchnorm_forward(outi,gammai,betai,self.bn_params[layer])
# bn_cache_list.append(bn_cachei)
# outi,relu_cachei = relu_forward(outi)
# relu_cache_list.append(relu_cachei)
#
# if self.use_dropout:
# outi,dropout_cachei = dropout_forward(outi,self.dropout_param)
# dropout_cache_list.append(dropout_cachei)
#
# inputi = outi
#
# scores = outi
if mode == 'test':
return scores
loss,grads = 0.0,{}
loss,dsoft = softmax_loss(scores,y)
loss += 0.5*self.reg*(np.sum(np.square(self.params['W'+str(self.num_layers)])))
#########最后一层的反向传播
dx_last,dw_last,db_last = affine_backward(dsoft,final_cache)
grads['W'+str(self.num_layers)] = dw_last+self.reg*self.params['W'+str(self.num_layers)]
grads['b'+str(self.num_layers)] = db_last
for i in range(self.num_layers-1,0,-1):
if self.use_dropout:
dx_last = dropout_backward(dx_last,dropout_cache_list[i-1])
drelu = relu_backward(dx_last,relu_cache_list[i-1])
if self.use_batchnorm:
dbatchnorm,dgamma,dbeta = batchnorm_backward(drelu,bn_cache_list[i-1])
dx_last,dw_last,db_last = affine_backward(dbatchnorm,fc_cache_list[i-1])
grads['beta'+str(i)] = dbeta
grads['gamma'+str(i)] = dgamma
else:
dx_last,dw_last,db_last = affine_backward(drelu,fc_cache_list[i-1])
grads['W'+str(i)] = dw_last+self.reg*self.params['W'+str(i)]
grads['b'+str(i)] = db_last
loss += 0.5*self.reg*(np.sum(np.square(self.params['W'+str(i)])))
return loss,grads
print('Testing relu_forward function:')
print('difference: ', rel_error(out, correct_out))
#######################################################################################
#######################################################################################
# Test the relu_backward function
#######################################################################################
from layers import relu_backward
x = np.random.randn(10, 10)
dout = np.random.randn(*x.shape)
dx_num = eval_numerical_gradient_array(lambda x: relu_forward(x)[0], x, dout)
_, cache = relu_forward(x)
dx = relu_backward(dout, cache)
# The error should be around 1e-12
print('Testing relu_backward function:')
print('dx error: ', rel_error(dx_num, dx))
#######################################################################################
#######################################################################################
# Test the sandwitch layers
# -If you implemented affine and relu functions properly,
# you would have no problem with this code
#######################################################################################
from layer_utils import affine_relu_forward
from layer_utils import affine_relu_backward
np.random.seed(231)
def loss(self, X, y=None):
"""
Compute loss and gradient for a minibatch of data.
Args:
- X: Input data, numpy array of shape (N, d_1, ..., d_k)
- y: Array of labels, of shape (N,). y[i] gives the label for X[i].
Returns:
If y is None, then run a test-time forward pass of the model and
return:
- scores: Array of shape (N, C) giving classification scores, where
scores[i, c] is the classification score for X[i] and class c.
If y is not None, then run a training-time forward and backward pass
and return a tuple of:
- loss: Scalar value giving the loss
- grads: Dictionary with the same keys as self.params, mapping
parameter
names to gradients of the loss with respect to those parameters.
"""
scores = None
X = X.astype(self.dtype)
linear_cache = dict()
relu_cache = dict()
dropout_cache = dict()
"""
TODO: Implement the forward pass for the fully-connected neural
network, compute the scores and store them in the scores variable.
"""
#######################################################################
# BEGIN OF YOUR CODE #
#######################################################################
# input -> first hidden layer
linear_cache[1] = linear_forward(X, self.params["W1"],
self.params["b1"])
input_next = relu_forward(linear_cache[1])
relu_cache[1] = input_next.copy()
# hidden layer i -> hidden layer i+1
for l in range(2, self.num_layers):
if self.use_dropout:
input_next, dropout_cache[l - 1] = self.apply_forward_dropout(
input_next)
linear_cache[l] = linear_forward(input_next,
self.params["W%d" % l],
self.params["b%d" % l])
input_next = relu_forward(linear_cache[l])
relu_cache[l] = input_next.copy()
# last hidden layer -> output layer
if self.use_dropout:
input_next, dropout_cache[
self.num_layers - 1] = self.apply_forward_dropout(input_next)
linear_cache[self.num_layers] = linear_forward(
input_next, self.params["W%d" % self.num_layers],
self.params["b%d" % self.num_layers])
scores = linear_cache[self.num_layers].copy()
# scores = scores / np.abs(scores).sum(axis=1)[:, None]
#print(scores)
# print(scores.shape)
#######################################################################
# END OF YOUR CODE #
#######################################################################
# If y is None then we are in test mode so just return scores
if y is None:
return scores
loss, grads = 0, dict()
"""
TODO: Implement the backward pass for the fully-connected net. Store
the loss in the loss variable and all gradients in the grads
dictionary. Compute the loss with softmax. grads[k] has the gradients
for self.params[k]. Add L2 regularisation to the loss function.
NOTE: To ensure that your implementation matches ours and you pass the
automated tests, make sure that your L2 regularization includes a
factor of 0.5 to simplify the expression for the gradient.
"""
#######################################################################
# BEGIN OF YOUR CODE #
#######################################################################
loss, dlogits = softmax(scores, y)
# add L2 regularization
loss += 0.5 * self.reg * np.sum([
np.sum(self.params["W%d" % l]**2)
for l in range(1, self.num_layers + 1)
])
# last hidden layer <- output layer
dX_, dW_, db_ = linear_backward(dlogits,
relu_cache[self.num_layers - 1],
self.params["W%d" % self.num_layers],
self.params["b%d" % self.num_layers])
# add regularization effect to W
grads["W%d" %
self.num_layers] = dW_ + self.reg * self.params["W%d" %
self.num_layers]
grads["b%d" % self.num_layers] = db_.copy()
# hidden layer i <- hidden layer i+1
for l in reversed(range(2, self.num_layers)):
if self.use_dropout:
dX_ = self.apply_backward_dropout(dX_, dropout_cache[l])
dX_ = relu_backward(dX_, linear_cache[l])
dX_, dW_, db_ = linear_backward(dX_, relu_cache[l - 1],
self.params["W%d" % l],
self.params["b%d" % l])
# add regularization effect to W
grads["W%d" % l] = dW_ + self.reg * self.params["W%d" % l]
grads["b%d" % l] = db_
# input layer <- first hidden layer
if self.use_dropout:
dX_ = self.apply_backward_dropout(dX_, dropout_cache[1])
dX_ = relu_backward(dX_, linear_cache[1])
dX_, dW_, db_ = linear_backward(dX_, X, self.params["W1"],
self.params["b1"])
# add regularization effect to W
grads["W1"] = dW_ + self.reg * self.params["W1"]
grads["b1"] = db_
#######################################################################
# END OF YOUR CODE #
#######################################################################
return loss, grads