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 affine_relu_backward(dout, cache):
"""
Backward pass for the affine-relu convenience layer
"""
fc_cache, relu_cache = cache
da = relu_backward(dout, relu_cache)
dx, dw, db = affine_backward(da, fc_cache)
return dx, dw, db
def affine_batchnorm_relu_backward(dout, cache):
"""
Backward pass for the Affine->BatchNorm->ReLU convenience layer
"""
fc_cache, bn_cache, relu_cache = cache
da = relu_backward(dout, relu_cache)
dan, dgamma, dbeta = batchnorm_backward(da, bn_cache)
dx, dw, db = affine_backward(dan, fc_cache)
return dx, dw, db, dgamma, dbeta
def affine_bn_relu_backward(dout, cache):
"""
Backward pass for the affine-bn-relu convenience layer
"""
fc_cache, bn_cache, relu_cache = cache
dx = layers.relu_backward(dout, relu_cache)
dx, dgamma, dbeta = layers.batchnorm_backward_alt(dx, bn_cache)
dx, dw, db = layers.affine_backward(dx, fc_cache)
return dx, dw, db, dgamma, dbeta
def combo_backward(dout, cache):
"""
Backward pass for the affine-relu convenience layer
"""
dgamma, dbeta = 0, 0
fc_cache, bn_cache, relu_cache = cache
da = relu_backward(dout, relu_cache)
if bn_cache is not None:
da, dgamma, dbeta = batchnorm_backward(da, bn_cache)
dx, dw, db = affine_backward(da, fc_cache)
return dx, dw, db, dgamma, dbeta
def rnn_step_full_backward(dcurrent_h, cache):
(x, prev_h, Wx, Wh, bh, Ws, bs, current_h, cache_affine, dscore) = cache
dcurrent_h_, dWs, dbs = affine_backward(dscore, cache_affine)
dcurrent_h = dcurrent_h + dcurrent_h_
dcurrent_state = dcurrent_h * (1 - np.square(current_h))
dx = dcurrent_state.dot(Wx.T)
dWx = x.T.dot(dcurrent_state)
dprev_h = dcurrent_state.dot(Wh.T)
dWh = prev_h.T.dot(dcurrent_state)
dbh = np.sum(dcurrent_state, axis=0)
return dx, dprev_h, dWx, dWh, dbh, dWs, dbs
def lstm_step_backward(dnext_h, dnext_c, cache):
"""
Backward pass for a single timestep of an LSTM.
Inputs:
- dnext_h: Gradients of next hidden state, of shape (N, H)
- dnext_c: Gradients of next cell state, of shape (N, H)
- cache: Values from the forward pass
Returns a tuple of:
- dx: Gradient of input data, of shape (N, D)
- dprev_h: Gradient of previous hidden state, of shape (N, H)
- dprev_c: Gradient of previous cell state, of shape (N, H)
- dWx: Gradient of input-to-hidden weights, of shape (D, 4H)
- dWh: Gradient of hidden-to-hidden weights, of shape (H, 4H)
- db: Gradient of biases, of shape (4H,)
"""
dx, dprev_h, dprev_c, dWx, dWh, db = None, None, None, None, None, None
#############################################################################
# TODO: Implement the backward pass for a single timestep of an LSTM. #
# #
# HINT: For sigmoid and tanh you can compute local derivatives in terms of #
# the output value from the nonlinearity. #
#############################################################################
N, H = dnext_h.shape
o, tanh_next_c, prev_c, cache_gates, i, f, o, g, D = cache
dtanh_next_c = dnext_h * o
dnext_c_sum = dtanh_next_c * (1 - tanh_next_c * tanh_next_c) + dnext_c
dprev_c = dnext_c_sum * f
di = dnext_c_sum * g
df = dnext_c_sum * prev_c
do = dnext_h * tanh_next_c
dg = dnext_c_sum * i
di_before_sigmoid = di * (i * (1 - i))
df_before_sigmoid = df * (f * (1 - f))
do_before_sigmoid = do * (o * (1 - o))
dg_before_tanh = dg * (1 - g * g)
d_gates = np.concatenate((di_before_sigmoid, df_before_sigmoid,
do_before_sigmoid, dg_before_tanh),
axis=1)
dinputs, dW, db = affine_backward(d_gates, cache_gates)
dWx = dW[:D, :]
dWh = dW[D:, :]
dx = dinputs[:, :D]
dprev_h = dinputs[:, D:]
##############################################################################
# END OF YOUR CODE #
##############################################################################
return dx, dprev_h, dprev_c, dWx, dWh, db
def test_affine_backward(): x = np.random.randn(10, 2, 3) w = np.random.randn(6, 5) b = np.random.randn(5) dout = np.random.randn(10, 5) dx_num = eval_numerical_gradient_array(lambda x: affine_forward(x, w, b)[0], x, dout) dw_num = eval_numerical_gradient_array(lambda w: affine_forward(x, w, b)[0], w, dout) db_num = eval_numerical_gradient_array(lambda b: affine_forward(x, w, b)[0], b, dout) _, cache = affine_forward(x, w, b) dx, dw, db = affine_backward(dout, cache) assert dx.shape == dx.shape assert dw.shape == dw.shape assert db.shape == db.shape assert rel_error(dx_num,dx) < 5e-7 assert rel_error(dw_num,dw) < 5e-7 assert rel_error(db_num,db) < 5e-7
def test_affine_backward():
x = np.random.randn(10, 2, 3)
w = np.random.randn(6, 5)
b = np.random.randn(5)
dout = np.random.randn(10, 5)
dx_num = eval_numerical_gradient_array(lambda x: affine_forward(x, w, b)[0], x, dout)
dw_num = eval_numerical_gradient_array(lambda w: affine_forward(x, w, b)[0], w, dout)
db_num = eval_numerical_gradient_array(lambda b: affine_forward(x, w, b)[0], b, dout)
_, cache = affine_forward(x, w, b)
dx, dw, db = affine_backward(dout, cache)
assert dx.shape == dx.shape
assert dw.shape == dw.shape
assert db.shape == db.shape
assert rel_error(dx_num,dx) < 5e-7
assert rel_error(dw_num,dw) < 5e-7
assert rel_error(db_num,db) < 5e-7
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_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
############################################################################
# TODO: Implement the forward pass for the two-layer net, computing the #
# class scores for X and storing them in the scores variable. #
############################################################################
hidden1_out, h1_cache = affine_forward(X, self.params['W1'],
self.params['b1'])
relu_out, relu_cache = relu_forward(hidden1_out)
scores, h2_cache = affine_forward(relu_out, self.params['W2'],
self.params['b2'])
############################################################################
# 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, {}
############################################################################
# TODO: Implement the backward pass for the two-layer net. Store the loss #
# in the loss variable and gradients in the grads dictionary. Compute data #
# loss using softmax, and make sure that grads[k] holds the gradients for #
# self.params[k]. Don't forget to add L2 regularization! #
# #
# 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. #
############################################################################
"""
X_reshape=np.reshape(X,(X.shape[0],-1))
num_trains=X.shape[0]
loss,_=softmax_loss(scores,y)
loss=loss+self.reg*0.5*(np.sum(self.params['W2']*self.params['W2'])+np.sum(self.params['W1']*self.params['W1']))
softmax_output=np.exp(scores)/np.sum(np.exp(scores),axis=1).reshape(-1,1)
softmax_output[range(num_trains),list(y)]=softmax_output[range(num_trains),list(y)]-1
grads['b2']=np.zeros_like(self.params['b2'])
grads['W2']=np.zeros_like(self.params['W2'])
grads['b1']=np.zeros_like(self.params['b1'])
grads['W1']=np.zeros_like(self.params['W1'])
grads['b2']=np.sum(softmax_output,axis=0)
grads['W2']=np.dot(relu_out.T,softmax_output)
grads_b1_tmp=np.dot(softmax_output,self.params['W2'].T)
tmp=(relu_out>0)*grads_b1_tmp
grads['b1']=np.sum(tmp,axis=0)
grads['W1']=np.dot(X_reshape.T,grads_b1_tmp)
grads['W1']=grads['W1']/num_trains+self.reg*self.params['W1']
grads['b1']=grads['b1']/num_trains
grads['W2']=grads['W2']/num_trains+self.reg*self.params['W2']
grads['b2']=grads['b2']/num_trains
"""
num_trains = X.shape[0]
loss, dscore = softmax_loss(scores, y)
loss = loss + self.reg * 0.5 * (
np.sum(self.params['W2'] * self.params['W2']) +
np.sum(self.params['W1'] * self.params['W1']))
grads_h2, grads_w2, grads_b2 = affine_backward(dout=dscore,
cache=h2_cache)
grads_relu = relu_backward(grads_h2, relu_cache)
grads_h1, grads_w1, grads_b1 = affine_backward(grads_relu, h1_cache)
grads['W1'] = grads_w1 + self.reg * self.params['W1']
grads['W2'] = grads_w2 + self.reg * self.params['W2']
grads['b1'] = grads_b1
grads['b2'] = grads_b2
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
def loss(self, X, y=None):
"""
Compute loss and gradient for the fully-connected net.
Inputs:
- X: Array of input data 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.
"""
X = X.astype(self.dtype)
mode = 'test' if y is None else 'train'
# Set train/test mode for batchnorm params and dropout param since they
# behave differently during training and testing.
if self.dropout_param is not None:
self.dropout_param['mode'] = mode
if self.use_batchnorm:
for bn_param in self.bn_params:
bn_param[mode] = mode
scores = None
#######################################################################
# TODO: Implement the forward pass for the fully-connected net,
# computing the class scores for X and storing them in the scores
# variable.
#
# When using dropout, you'll need to pass self.dropout_param to each
# dropout forward pass.
#
# When using batch normalization, you'll need to pass self.bn_params[0]
# to the forward pass for the first batch normalization layer,
# pass self.bn_params[1] to the forward pass for the second batch
# normalization layer, etc.
#######################################################################
IN = X
caches = {}
if self.use_dropout:
dropout_caches = {}
for l in range(self.num_layers - 1):
W = self.params["W{}".format(l + 1)]
b = self.params["b{}".format(l + 1)]
if self.use_batchnorm:
gamma = self.params["gamma{}".format(l + 1)]
beta = self.params["beta{}".format(l + 1)]
IN, cache = affine_batchnorm_relu_forward(
IN, W, b, gamma, beta, self.bn_params[l])
else:
IN, cache = affine_relu_forward(IN, W, b)
caches[l] = cache
if self.use_dropout:
IN, d_cache = dropout_forward(IN, self.dropout_param)
dropout_caches[l] = d_cache
# forward pass: last affine layer
num_last = self.num_layers
name_W_last = "W{}".format(num_last)
name_b_last = "b{}".format(num_last)
W_last = self.params[name_W_last]
b_last = self.params[name_b_last]
scores, cache_last = affine_forward(IN, W_last, b_last)
#######################################################################
# END OF YOUR CODE #
#######################################################################
# If test mode return early
if mode == 'test':
return scores
loss, grads = 0.0, {}
#######################################################################
# TODO: Implement the backward pass for the fully-connected net.
# Store the loss in the loss variable and gradients in the grads
# dictionary. Compute data loss using softmax, and make sure that
# grads[k] holds the gradients for self.params[k]. Don't forget to add
# L2 regularization!
#
# When using batch normalization, you don't need to regularize the
# scale and shift parameters.
#
# 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.
#######################################################################
# loss
loss, dscores = softmax_loss(scores, y)
# regularization loss
for l in range(self.num_layers):
W = self.params["W{}".format(l + 1)]
loss += 0.5 * self.reg * np.sum(W * W)
# backprop through last affine layer
dx, dw, db = affine_backward(dscores, cache_last)
grads[name_W_last] = dw + self.reg * W_last
grads[name_b_last] = db
# backprop through affine-batchnorm-relu layers
for l in reversed(range(self.num_layers - 1)):
name_W = "W{}".format(l + 1)
name_b = "b{}".format(l + 1)
if self.use_dropout:
dx = dropout_backward(dx, dropout_caches[l])
if self.use_batchnorm:
dx, dw, db, dgamma, dbeta = affine_batchnorm_relu_backward(
dx, caches[l])
grads["gamma{}".format(l + 1)] = dgamma
grads["beta{}".format(l + 1)] = dbeta
else:
dx, dw, db = affine_relu_backward(dx, caches[l])
grads[name_W] = dw + self.reg * self.params[name_W]
grads[name_b] = db
#######################################################################
# END OF YOUR CODE #
#######################################################################
return loss, grads
def two_layer_net(X, model, y=None, reg=0.0):
"""
Compute the loss and gradients for a two layer fully connected neural network.
The net has an input dimension of D, a hidden layer dimension of H, and
performs classification over C classes. We use a softmax loss function and L2
regularization the the weight matrices. The two layer net should use a ReLU
nonlinearity after the first affine layer.
The two layer net has the following architecture:
input - fully connected layer - ReLU - fully connected layer - softmax
The outputs of the second fully-connected layer are the scores for each
class.
Inputs:
- X: Input data of shape (N, D). Each X[i] is a training sample.
- model: Dictionary mapping parameter names to arrays of parameter values.
It should contain the following:
- W1: First layer weights; has shape (D, H)
- b1: First layer biases; has shape (H,)
- W2: Second layer weights; has shape (H, C)
- b2: Second layer biases; has shape (C,)
- y: Vector of training labels. y[i] is the label for X[i], and each y[i] is
an integer in the range 0 <= y[i] < C. This parameter is optional; if it
is not passed then we only return scores, and if it is passed then we
instead return the loss and gradients.
- reg: Regularization strength.
Returns:
If y not is passed, return a matrix scores of shape (N, C) where scores[i, c]
is the score for class c on input X[i].
If y is not passed, instead return a tuple of:
- loss: Loss (data loss and regularization loss) for this batch of training
samples.
- grads: Dictionary mapping parameter names to gradients of those parameters
with respect to the loss function. This should have the same keys as model.
"""
# unpack variables from the model dictionary
W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
N, D = X.shape
# compute the forward pass
scores = None
#############################################################################
# TODO: Perform the forward pass, computing the class scores for the input. #
# Store the result in the scores variable, which should be an array of #
# shape (N, C). #
#############################################################################
# relu = lambda x: np.maximum(x,0)
# H, C = W2.shape
# scores = np.zeros((N,C))
# layer1 = np.maximum(np.dot(X,W1) + b1,0)
# scores = np.dot(layer1,W2) + b2
## above is the test implementation
## NOW, using cs231n/layers.py
## NOTICE define layer0 = X
# then behaviour is 'functional' layer(n+1) = f(layer(n) | parameters)
from cs231n.layers import affine_forward, relu_forward, softmax_loss
from cs231n.layers import affine_backward, relu_backward
layer1, cache1 = affine_forward(X, W1, b1)
layer2, cache2 = relu_forward(layer1)
layer3, cache3 = affine_forward(layer2, W2, b2)
scores = layer3
#############################################################################
# END OF YOUR CODE #
#############################################################################
# If the targets are not given then jump out, we're done
if y is None:
return scores
# compute the loss
loss = None
#############################################################################
# TODO: Finish the forward pass, and compute the loss. This should include #
# both the data loss and L2 regularization for W1 and W2. Store the result #
# in the variable loss, which should be a scalar. Use the Softmax #
# classifier loss. So that your results match ours, multiply the #
# regularization loss by 0.5 #
#############################################################################
# rows = np.sum(np.exp(scores), axis=1)
# layer4 = np.mean(-layer3[range(N), y] + np.log(rows))
# loss = layer4 + 0.5 * reg * (np.sum(W1 * W1) + np.sum(W2 * W2))
#
loss, dx = softmax_loss(scores, y)
loss += 0.5 * reg * np.sum(W1*W1) + 0.5 * reg * np.sum(W2 * W2)
#############################################################################
# END OF YOUR CODE #
#############################################################################
# compute the gradients
grads = {}
#############################################################################
# TODO: Compute the backward pass, computing the derivatives of the weights #
# and biases. Store the results in the grads dictionary. For example, #
# grads['W1'] should store the gradient on W1, and be a matrix of same size #
#############################################################################
dlayer2, grads['W2'], grads['b2'] = affine_backward(dx, cache3)
dlayer1 = relu_backward(dlayer2, cache2)
dLayer0, grads['W1'], grads['b1'] = affine_backward(dlayer1, cache1)
#gradients need to have regularization term
grads['W2'] += reg * W2
grads['W1'] += reg * W1
#############################################################################
# END OF YOUR CODE #
#############################################################################
return loss, 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_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
############################################################################
# TODO: Implement the forward pass for the two-layer net, computing the #
# class scores for X and storing them in the scores variable. #
############################################################################
out_affine1, cache_affine1 = layers.affine_forward(
X, self.params["W1"], self.params["b1"])
out_relu1, cache_relu1 = layers.relu_forward(out_affine1)
out_affine2, cache_affine2 = layers.affine_forward(
out_relu1, self.params["W2"], self.params["b2"])
# no need to compute SVM/softmax loss, just give the argmax result When
# we are in prediction.
scores = out_affine2
############################################################################
# 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, {}
############################################################################
# TODO: Implement the backward pass for the two-layer net. Store the loss #
# in the loss variable and gradients in the grads dictionary. Compute data #
# loss using softmax, and make sure that grads[k] holds the gradients for #
# self.params[k]. Don't forget to add L2 regularization! #
# #
# 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. #
############################################################################
# in training, compute the loss and do backprop.
loss, dloss = layers.softmax_loss(scores, y)
# need to add regularization here...
loss += 0.5 * self.reg * (np.sum(self.params["W1"]**2) +
np.sum(self.params["W2"]**2))
dout_affine2 = layers.affine_backward(dloss, cache_affine2)
grads["W2"] = dout_affine2[1] + self.reg * self.params["W2"]
grads["b2"] = dout_affine2[2]
dout_relu1 = layers.relu_backward(dout_affine2[0], cache_relu1)
dout_affine1 = layers.affine_backward(dout_relu1, cache_affine1)
grads["W1"] = dout_affine1[1] + self.reg * self.params["W1"]
grads["b1"] = dout_affine1[2]
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
def loss(self, X, y=None):
"""
Compute loss and gradient for the fully-connected net.
Input / output: Same as TwoLayerNet above.
"""
X = X.astype(self.dtype)
mode = 'test' if y is None else 'train'
# Set train/test mode for batchnorm params and dropout param since they
# behave differently during training and testing.
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
############################################################################
# TODO: Implement the forward pass for the fully-connected net, computing #
# the class scores for X and storing them in the scores variable. #
# #
# When using dropout, you'll need to pass self.dropout_param to each #
# dropout forward pass. #
# #
# When using batch normalization, you'll need to pass self.bn_params[0] to #
# the forward pass for the first batch normalization layer, pass #
# self.bn_params[1] to the forward pass for the second batch normalization #
# layer, etc. #
############################################################################
caches = collections.defaultdict(list)
out_layer = X
for i in range(self.num_layers - 1):
n = str(i + 1)
# (zy) The learned parameters are for BN affine transformation used
# in training, while the running average is used for prediction.
if self.use_batchnorm:
out_layer, cache = affine_bn_relu_forward(
out_layer, self.params["W" + n], self.params["b" + n],
self.params["gamma" + n], self.params["beta" + n],
self.bn_params[i])
caches["affine_bn_relu"].append(cache)
else:
out_layer, cache = layers.affine_forward(
out_layer, self.params["W" + n], self.params["b" + n])
caches["affine"].append(cache)
out_layer, cache = layers.relu_forward(out_layer)
caches["relu"].append(cache)
if self.use_dropout:
out_layer, cache = layers.dropout_forward(
out_layer, self.dropout_param)
caches["drop"].append(cache)
nn = str(self.num_layers)
scores, cache = layers.affine_forward(out_layer, self.params["W" + nn],
self.params["b" + nn])
############################################################################
# END OF YOUR CODE #
############################################################################
# If test mode return early
if mode == 'test':
return scores
loss, grads = 0.0, {}
############################################################################
# TODO: Implement the backward pass for the fully-connected net. Store the #
# loss in the loss variable and gradients in the grads dictionary. Compute #
# data loss using softmax, and make sure that grads[k] holds the gradients #
# for self.params[k]. Don't forget to add L2 regularization! #
# #
# When using batch normalization, you don't need to regularize the scale #
# and shift parameters. #
# #
# 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. #
############################################################################
loss, dloss = layers.softmax_loss(scores, y)
# for regularization
if self.reg != 0:
for k, v in self.params.items():
# only include the w parameters, excluding gamma, beta and b
if k.startswith("W"):
loss += 0.5 * self.reg * np.sum(v**2)
# get the gradient
out = layers.affine_backward(dloss, cache)
dout, grads["W" + nn], grads["b" + nn] = out
grads["W" + nn] += self.reg * cache[1]
for i in range(self.num_layers - 2, -1, -1):
n = str(i + 1)
if self.use_dropout:
dout = layers.dropout_backward(dout, caches["drop"][i])
if self.use_batchnorm:
out = affine_bn_relu_backward(dout,
caches["affine_bn_relu"][i])
dout, grads["W"+n], grads["b"+n], \
grads["gamma"+n], grads["beta"+n] = out
grads["W" +
n] += self.reg * self.params["W" + n] if self.reg else 0
else:
dout = layers.relu_backward(dout, caches["relu"][i])
out = layers.affine_backward(dout, caches["affine"][i])
dout, grads["W" + n], grads["b" + n] = out
# need to include regularization
grads["W" + n] += self.reg * caches["affine"][i][1]
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
def loss(self, X, y=None):
"""
Compute loss and gradient for the fully-connected net.
Input / output: Same as TwoLayerNet above.
"""
X = X.astype(self.dtype)
mode = 'test' if y is None else 'train'
# Set train/test mode for batchnorm params and dropout param since they
# behave differently during training and testing.
if self.use_dropout:
self.dropout_param['mode'] = mode
if self.normalization == 'batchnorm':
for bn_param in self.bn_params:
bn_param['mode'] = mode
scores = None
############################################################################
# TODO: Implement the forward pass for the fully-connected net, computing #
# the class scores for X and storing them in the scores variable. #
# #
# When using dropout, you'll need to pass self.dropout_param to each #
# dropout forward pass. #
# #
# When using batch normalization, you'll need to pass self.bn_params[0] to #
# the forward pass for the first batch normalization layer, pass #
# self.bn_params[1] to the forward pass for the second batch normalization #
# layer, etc. #
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
arg, caches = X, []
for i in range(1, self.num_layers + 1):
cache = {}
W = self.params[f"W{i}"]
b = self.params[f"b{i}"]
arg, cache['fc_cache'] = affine_forward(arg, W, b)
if i != self.num_layers and self.normalization:
gamma = self.params[f"gamma{i}"]
beta = self.params[f"beta{i}"]
normalize_forward = batchnorm_forward if self.normalization is 'batchnorm' else layernorm_forward
arg, cache['bn_cache'] = normalize_forward(arg, gamma, beta, self.bn_params[i-1])
arg, cache['relu_cache'] = relu_forward(arg)
if self.use_dropout:
arg, cache['dropout_cache'] = dropout_forward(arg, self.dropout_param)
caches.append(cache)
scores = arg
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
# If test mode return early
if mode == 'test':
return scores
loss, grads = 0.0, {}
############################################################################
# TODO: Implement the backward pass for the fully-connected net. Store the #
# loss in the loss variable and gradients in the grads dictionary. Compute #
# data loss using softmax, and make sure that grads[k] holds the gradients #
# for self.params[k]. Don't forget to add L2 regularization! #
# #
# When using batch/layer normalization, you don't need to regularize the scale #
# and shift parameters. #
# #
# 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. #
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
loss, dout = softmax_loss(scores, y)
for i in range(self.num_layers, 0, -1):
W = self.params[f"W{i}"]
cache = caches[i-1]
if self.use_dropout:
dout = dropout_backward(dout, cache['dropout_cache'])
da = relu_backward(dout, cache['relu_cache'])
if i != self.num_layers and self.normalization:
normalize_backward = batchnorm_backward if self.normalization is 'batchnorm' else layernorm_backward
da, dgamma, dbeta = batchnorm_backward(da, cache['bn_cache'])
grads[f"gamma{i}"] = dgamma
grads[f"beta{i}"] = dbeta
dout, dw, db = affine_backward(da, cache['fc_cache'])
grads[f"W{i}"] = dw + self.reg * W
grads[f"b{i}"] = db
loss += 0.5 * self.reg * np.sum(W * W)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
# Test the affine_backward function
np.random.seed(231)
x = np.random.randn(10, 2, 3)
w = np.random.randn(6, 5)
b = np.random.randn(5)
dout = np.random.randn(10, 5)
dx_num = eval_numerical_gradient_array(lambda x: affine_forward(x, w, b)[0], x,
dout)
dw_num = eval_numerical_gradient_array(lambda w: affine_forward(x, w, b)[0], w,
dout)
db_num = eval_numerical_gradient_array(lambda b: affine_forward(x, w, b)[0], b,
dout)
_, cache = affine_forward(x, w, b)
dx, dw, db = affine_backward(dout, cache)
# The error should be around 1e-10
print('Testing affine_backward function:')
print('dx error: ', rel_error(dx_num, dx))
print('dw error: ', rel_error(dw_num, dw))
print('db error: ', rel_error(db_num, db))
# Test the relu_forward function
x = np.linspace(-0.5, 0.5, num=12).reshape(3, 4)
out, _ = relu_forward(x)
correct_out = np.array([[
0.,
0.,
0.,
def loss(self, X, y=None):
"""
Compute loss and gradient for the fully-connected net.
Input / output: Same as TwoLayerNet above.
"""
X = X.astype(self.dtype)
mode = 'test' if y is None else 'train'
# Set train/test mode for batchnorm params and dropout param since they
# behave differently during training and testing.
if self.use_dropout:
self.dropout_param['mode'] = mode
if self.normalization == 'batchnorm':
for bn_param in self.bn_params:
bn_param['mode'] = mode
scores = None
############################################################################
# TODO: Implement the forward pass for the fully-connected net, computing #
# the class scores for X and storing them in the scores variable. #
# #
# When using dropout, you'll need to pass self.dropout_param to each #
# dropout forward pass. #
# #
# When using batch normalization, you'll need to pass self.bn_params[0] to #
# the forward pass for the first batch normalization layer, pass #
# self.bn_params[1] to the forward pass for the second batch normalization #
# layer, etc. #
############################################################################
combo_caches = []
fc_cache = None
N = X.shape[0]
D = np.prod(X.shape[1:])
x_ = X.reshape(N, D)
# middle combo layers
for layer in range(1, self.num_layers): #[1, 2, ..., L-1]
w = self.params['W' + str(layer)]
b = self.params['b' + str(layer)]
# prepare for batch normalization
gamma, beta, bn_parma = 1., 0, None
if self.normalization == 'batchnorm':
gamma = self.params['gamma' + str(layer)]
beta = self.params['beta' + str(layer)]
bn_parma = self.bn_params[layer - 1] # zero based
x_, cache = combo_forward(x_, w, b, gamma, beta, bn_parma)
combo_caches.append(cache)
# final fully connected layer
w = self.params['W' + str(self.num_layers)]
b = self.params['b' + str(self.num_layers)]
scores, fc_cache = affine_forward(x_, w, b)
############################################################################
# END OF YOUR CODE #
############################################################################
# If test mode return early
if mode == 'test':
return scores
loss, grads = 0.0, {}
############################################################################
# TODO: Implement the backward pass for the fully-connected net. Store the #
# loss in the loss variable and gradients in the grads dictionary. Compute #
# data loss using softmax, and make sure that grads[k] holds the gradients #
# for self.params[k]. Don't forget to add L2 regularization! #
# #
# When using batch/layer normalization, you don't need to regularize the scale #
# and shift parameters. #
# #
# 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. #
############################################################################
loss, dout = softmax_loss(scores, y)
# finall fully connected layer
dout, dw, db = affine_backward(dout, fc_cache)
grads['W' +
str(self.num_layers
)] = dw + self.reg * self.params['W' + str(self.num_layers)]
grads['b' + str(self.num_layers)] = db
# adjust loss with regularization term of dWL
loss += 0.5 * self.reg * np.sum(self.params['W' + str(self.num_layers)]
**2)
# middle combo layers
for layer in range(self.num_layers - 1, 0, -1): # [L-1, L-2, ... ,1]
dout, dw, db, dgamma, dbeta = combo_backward(
dout, combo_caches[layer - 1])
grads['W' +
str(layer)] = dw + self.reg * self.params['W' + str(layer)]
grads['b' + str(layer)] = db
if self.normalization == 'batchnorm':
grads['gamma' + str(layer)] = dgamma
grads['beta' + str(layer)] = dbeta
# adjust loss with regularization term of dWl
loss += 0.5 * self.reg * np.sum(self.params['W' + str(layer)]**2)
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, 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_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
#######################################################################
# TODO: Implement the forward pass for the two-layer net, computing the
# class scores for X and storing them in the scores variable.
#######################################################################
W1 = self.params["W1"]
b1 = self.params["b1"]
W2 = self.params["W2"]
b2 = self.params["b2"]
N = X.shape[0]
C = W2.shape[1]
scores = np.zeros((N, C))
X_hidden, cache1 = affine_relu_forward(X, W1, b1)
scores, cache2 = affine_forward(X_hidden, W2, b2)
#######################################################################
# 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, {}
#######################################################################
# TODO: Implement the backward pass for the two-layer net. Store the
# loss in the loss variable and gradients in the grads dictionary.
# Compute data loss using softmax, and make sure that grads[k]
# holds the gradients for self.params[k]. Don't forget to add L2
# regularization!
#
# 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.
#######################################################################
loss, dscores = softmax_loss(scores, y)
loss += 0.5 * self.reg * (np.sum(W1 * W1) + np.sum(W2 * W2))
dx_hidden, dw2, db2 = affine_backward(dscores, cache2)
grads["W2"] = dw2 + self.reg * W2
grads["b2"] = db2
dx, dw1, db1 = affine_relu_backward(dx_hidden, cache1)
grads["W1"] = dw1 + self.reg * W1
grads["b1"] = db1
#######################################################################
# END OF YOUR CODE #
#######################################################################
return loss, 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_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
############################################################################
# TODO: Implement the forward pass for the two-layer net, computing the #
# class scores for X and storing them in the scores variable. #
############################################################################
W1, b1 = self.params['W1'], self.params['b1']
W2, b2 = self.params['W2'], self.params['b2']
N = X.shape[0]
D = np.prod(X.shape[1:])
X_ = X.reshape(N, D)
A, fc1_cache = affine_forward(X_, W1, b1)
R, relu_cache = relu_forward(A)
scores, fc2_cache = affine_forward(R, W2, b2)
############################################################################
# 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, {}
############################################################################
# TODO: Implement the backward pass for the two-layer net. Store the loss #
# in the loss variable and gradients in the grads dictionary. Compute data #
# loss using softmax, and make sure that grads[k] holds the gradients for #
# self.params[k]. Don't forget to add L2 regularization! #
# #
# 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. #
############################################################################
loss, dscores = softmax_loss(scores, y)
dR, dW2, db2 = affine_backward(dscores, fc2_cache)
dA = relu_backward(dR, relu_cache)
dX, dW1, db1 = affine_backward(dA, fc1_cache)
loss += 0.5 * self.reg * (np.sum(W1 * W1) + np.sum(W2 * W2))
dW2 += self.reg * W2
dW1 += self.reg * W1
grads = {'W1': dW1, 'b1': db1, 'W2': dW2, 'b2': db2}
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
def loss(self, X, y=None):
"""
Compute loss and gradient for the fully-connected net.
Input / output: Same as TwoLayerNet above.
"""
X = X.astype(self.dtype)
mode = 'test' if y is None else 'train'
# Set train/test mode for batchnorm params and dropout param since they
# behave differently during training and testing.
"""
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
############################################################################
# TODO: Implement the forward pass for the fully-connected net, computing #
# the class scores for X and storing them in the scores variable. #
# #
# When using dropout, you'll need to pass self.dropout_param to each #
# dropout forward pass. #
# #
# When using batch normalization, you'll need to pass self.bn_params[0] to #
# the forward pass for the first batch normalization layer, pass #
# self.bn_params[1] to the forward pass for the second batch normalization #
# layer, etc. #
############################################################################
X_temp = X
affine_Input = list()
relu_input = list()
batchnorm_input = list()
dropout_input = list()
score_tmp = None
for i in range(self.num_layers - 1):
tmp, affine_input_tmp = affine_forward(
X_temp, self.params['W' + str(i + 1)],
self.params['b' + str(i + 1)])
if self.use_batchnorm:
tmp, batchnorm_cache = batchnorm_forward(
tmp, self.params['gamma' + str(i + 1)],
self.params['beta' + str(i + 1)], self.bn_params[i])
batchnorm_input.append(batchnorm_cache)
score_tmp, relu_input_tmp = relu_forward(tmp)
if self.use_dropout:
score_tmp, dropout_cache = dropout_forward(
score_tmp, self.dropout_param)
dropout_input.append(dropout_cache)
affine_Input.append(affine_input_tmp)
relu_input.append(relu_input_tmp)
X_temp = score_tmp
scores, last_input_tmp = affine_forward(
score_tmp, self.params['W' + str(self.num_layers)],
self.params['b' + str(self.num_layers)])
affine_Input.append(last_input_tmp)
############################################################################
# END OF YOUR CODE #
############################################################################
if mode == 'test':
return scores
loss, grads = 0.0, {}
############################################################################
# TODO: Implement the backward pass for the fully-connected net. Store the #
# loss in the loss variable and gradients in the grads dictionary. Compute #
# data loss using softmax, and make sure that grads[k] holds the gradients #
# for self.params[k]. Don't forget to add L2 regularization! #
# #
# When using batch normalization, you don't need to regularize the scale #
# and shift parameters. #
# #
# 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. #
############################################################################
num_trains = X.shape[0]
loss, dscores = softmax_loss(scores, y)
weight_decay_sum = 0
for i in range(self.num_layers):
tmp = np.sum(self.params['W' + str(i + 1)] *
self.params['W' + str(i + 1)])
weight_decay_sum = weight_decay_sum + tmp
loss = loss + 0.5 * self.reg * weight_decay_sum
#softmax_output=np.exp(scores)/np.sum(np.exp(scores),axis=1).reshape(-1,1)
#softmax_output[range(num_trains),list(y)]=softmax_output[range(num_trains),list(y)]-1
dout = dscores
for i in range(self.num_layers):
dx, dw, db = affine_backward(dout, affine_Input[-(i + 1)])
grads['W' +
str(self.num_layers - i)] = dw + self.reg * self.params[
'W' + str(self.num_layers - i)]
grads['b' + str(self.num_layers - i)] = db
if self.use_dropout and i != self.num_layers - 1:
dx = dropout_backward(dx, dropout_input[-(i + 1)])
if i != self.num_layers - 1:
dout = relu_backward(dx, relu_input[-(i + 1)])
if i != self.num_layers - 1 and self.use_batchnorm:
dout, dgamma, dbeta = batchnorm_backward(
dout, batchnorm_input[-(i + 1)])
grads['gamma' + str(self.num_layers - i - 1)] = dgamma
grads['beta' + str(self.num_layers - i - 1)] = dbeta
return loss, grads