代码实现题代码
daseCV/layers.py
from builtins import range
import numpy as np
def affine_forward(x, w, b):
"""
为仿射(全连接)层计算前向传播
输入x的形状为(N, d_1, ..., d_k)，其中包含了N个样本，
每个样本x[i]都有形状(d_1, ..., d_k)。我们把每个输入重新reshape成为一个D维向量
D = d_1 * ... * d_k，然后将其转换为M维的输出向量。
Inputs:
- x: A numpy array containing input data, of shape (N, d_1, ..., d_k)
- w: A numpy array of weights, of shape (D, M)
- b: A numpy array of biases, of shape (M,)
Returns a tuple of:
- out: output, of shape (N, M)
- cache: (x, w, b)
"""
out = None
###########################################################################
# TODO: Implement the affine forward pass. Store the result in out. You #
# will need to reshape the input into rows. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
N = x.shape[0]
out = x.reshape(N, -1).dot(w) + b
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = (x, w, b)
return out, cache
def affine_backward(dout, cache):
"""
为仿射层计算反向传播
Inputs:
- dout: Upstream derivative, of shape (N, M)
- cache: Tuple of:
- x: Input data, of shape (N, d_1, ... d_k)
- w: Weights, of shape (D, M)
- b: Biases, of shape (M,)
Returns a tuple of:
- dx: Gradient with respect to x, of shape (N, d1, ..., d_k)
- dw: Gradient with respect to w, of shape (D, M)
- db: Gradient with respect to b, of shape (M,)
"""
x, w, b = cache
dx, dw, db = None, None, None
###########################################################################
# TODO: Implement the affine backward pass. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
N = x.shape[0]
dx = dout.dot(w.T) # shape(N, D)
dx = dx.reshape(x.shape)
dw = x.reshape(N, -1).T.dot(dout)
db = dout.T.dot(np.ones((N)))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
def relu_forward(x):
"""
计算一层整流线性单元(ReLUs)的前向传播。
Input:
- x: Inputs, of any shape
Returns a tuple of:
- out: Output, of the same shape as x
- cache: x
"""
out = None
###########################################################################
# TODO: Implement the ReLU forward pass. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
out = np.maximum(x, 0)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = x
return out, cache
def relu_backward(dout, cache):
"""
Computes the backward pass for a layer of rectified linear units (ReLUs).
Input:
- dout: Upstream derivatives, of any shape
- cache: Input x, of same shape as dout
Returns:
- dx: Gradient with respect to x
"""
dx, x = None, cache
###########################################################################
# TODO: Implement the ReLU backward pass. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
relu_x = np.maximum(x, 0)
relu_x[relu_x > 0] = 1
dx = relu_x * dout
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
def batchnorm_forward(x, gamma, beta, bn_param):
"""
Forward pass for batch normalization.
During training the sample mean and (uncorrected) sample variance are
computed from minibatch statistics and used to normalize the incoming data.
During training we also keep an exponentially decaying running mean of the
mean and variance of each feature, and these averages are used to normalize
data at test-time.
At each timestep we update the running averages for mean and variance using
an exponential decay based on the momentum parameter:
running_mean = momentum * running_mean + (1 - momentum) * sample_mean
running_var = momentum * running_var + (1 - momentum) * sample_var
Note that the batch normalization paper suggests a different test-time
behavior: they compute sample mean and variance for each feature using a
large number of training images rather than using a running average. For
this implementation we have chosen to use running averages instead since
they do not require an additional estimation step; the torch7
implementation of batch normalization also uses running averages.
Input:
- x: Data of shape (N, D)
- gamma: Scale parameter of shape (D,)
- beta: Shift paremeter of shape (D,)
- bn_param: Dictionary with the following keys:
- mode: 'train' or 'test'; required
- eps: Constant for numeric stability
- momentum: Constant for running mean / variance.
- running_mean: Array of shape (D,) giving running mean of features
- running_var Array of shape (D,) giving running variance of features
Returns a tuple of:
- out: of shape (N, D)
- cache: A tuple of values needed in the backward pass
"""
mode = bn_param['mode']
eps = bn_param.get('eps', 1e-5)
momentum = bn_param.get('momentum', 0.9)
N, D = x.shape
running_mean = bn_param.get('running_mean', np.zeros(D, dtype=x.dtype))
running_var = bn_param.get('running_var', np.zeros(D, dtype=x.dtype))
out, cache = None, None
if mode == 'train':
#######################################################################
# TODO: Implement the training-time forward pass for batch norm. #
# Use minibatch statistics to compute the mean and variance, use #
# these statistics to normalize the incoming data, and scale and #
# shift the normalized data using gamma and beta. #
# #
# You should store the output in the variable out. Any intermediates #
# that you need for the backward pass should be stored in the cache #
# variable. #
# #
# You should also use your computed sample mean and variance together #
# with the momentum variable to update the running mean and running #
# variance, storing your result in the running_mean and running_var #
# variables. #
# #
# Note that though you should be keeping track of the running #
# variance, you should normalize the data based on the standard #
# deviation (square root of variance) instead! #
# Referencing the original paper (https://arxiv.org/abs/1502.03167) #
# might prove to be helpful. #
#######################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
sample_mean, sample_var = np.mean(x, axis=0), np.var(x, axis=0)
x_hat = (x - sample_mean) / np.sqrt(sample_var + eps)
out = gamma * x_hat + beta
running_mean = momentum * running_mean + (1 - momentum) * sample_mean
running_var = momentum * running_var + (1 - momentum) * sample_var
cache = (x, x_hat, gamma, sample_mean, np.sqrt(sample_var+eps))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#######################################################################
# END OF YOUR CODE #
#######################################################################
elif mode == 'test':
#######################################################################
# TODO: Implement the test-time forward pass for batch normalization. #
# Use the running mean and variance to normalize the incoming data, #
# then scale and shift the normalized data using gamma and beta. #
# Store the result in the out variable. #
#######################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
x_hat = (x - running_mean) / np.sqrt(running_var + eps)
out = gamma * x_hat + beta
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#######################################################################
# END OF YOUR CODE #
#######################################################################
else:
raise ValueError('Invalid forward batchnorm mode "%s"' % mode)
# Store the updated running means back into bn_param
bn_param['running_mean'] = running_mean
bn_param['running_var'] = running_var
return out, cache
def batchnorm_backward(dout, cache):
"""
Backward pass for batch normalization.
For this implementation, you should write out a computation graph for
batch normalization on paper and propagate gradients backward through
intermediate nodes.
Inputs:
- dout: Upstream derivatives, of shape (N, D)
- cache: Variable of intermediates from batchnorm_forward.
Returns a tuple of:
- dx: Gradient with respect to inputs x, of shape (N, D)
- dgamma: Gradient with respect to scale parameter gamma, of shape (D,)
- dbeta: Gradient with respect to shift parameter beta, of shape (D,)
"""
dx, dgamma, dbeta = None, None, None
###########################################################################
# TODO: Implement the backward pass for batch normalization. Store the #
# results in the dx, dgamma, and dbeta variables. #
# Referencing the original paper (https://arxiv.org/abs/1502.03167) #
# might prove to be helpful. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
x, x_hat, gamma, sample_mean, std = cache
N, D = x.shape
dgamma = np.sum(dout * x_hat, axis=0)
dbeta = np.sum(dout, axis=0)
dx_hat = dout * gamma
dx_1 = dx_hat / std
dsigma = np.sum(dx_hat * (x - sample_mean), axis=0) * (-0.5 * (std ** -3))
dsigma_mu = -2/N * np.sum(x - sample_mean, axis=0)
dmu = -np.sum(dx_hat / std, axis=0) + dsigma * dsigma_mu
dmu_x = 1 / N
dsigma_x = 2/N * (x - sample_mean)
dx = dx_1 + dmu * dmu_x + dsigma * dsigma_x
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dgamma, dbeta
def batchnorm_backward_alt(dout, cache):
"""
Alternative backward pass for batch normalization.
For this implementation you should work out the derivatives for the batch
normalizaton backward pass on paper and simplify as much as possible. You
should be able to derive a simple expression for the backward pass.
See the jupyter notebook for more hints.
Note: This implementation should expect to receive the same cache variable
as batchnorm_backward, but might not use all of the values in the cache.
Inputs / outputs: Same as batchnorm_backward
"""
dx, dgamma, dbeta = None, None, None
###########################################################################
# TODO: Implement the backward pass for batch normalization. Store the #
# results in the dx, dgamma, and dbeta variables. #
# #
# After computing the gradient with respect to the centered inputs, you #
# should be able to compute gradients with respect to the inputs in a #
# single statement; our implementation fits on a single 80-character line.#
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
x, x_hat, gamma, sample_mean, std = cache
N, D = x.shape
dgamma = np.sum(dout * x_hat, axis=0)
dbeta = np.sum(dout, axis=0)
dx_hat = dout * gamma
dsigma2 = -0.5*np.sum(dx_hat*(x-sample_mean), axis=0)*std**(-3)
dmu = -np.sum(dx_hat/std, axis=0) - 2*dsigma2*np.mean(x-sample_mean, axis=0)
dx = dx_hat/std + 2/N*dsigma2*(x-sample_mean) + dmu/N
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dgamma, dbeta
def layernorm_forward(x, gamma, beta, ln_param):
"""
Forward pass for layer normalization.
During both training and test-time, the incoming data is normalized per data-point,
before being scaled by gamma and beta parameters identical to that of batch normalization.
Note that in contrast to batch normalization, the behavior during train and test-time for
layer normalization are identical, and we do not need to keep track of running averages
of any sort.
Input:
- x: Data of shape (N, D)
- gamma: Scale parameter of shape (D,)
- beta: Shift paremeter of shape (D,)
- ln_param: Dictionary with the following keys:
- eps: Constant for numeric stability
Returns a tuple of:
- out: of shape (N, D)
- cache: A tuple of values needed in the backward pass
"""
out, cache = None, None
eps = ln_param.get('eps', 1e-5)
###########################################################################
# TODO: Implement the training-time forward pass for layer norm. #
# Normalize the incoming data, and scale and shift the normalized data #
# using gamma and beta. #
# HINT: this can be done by slightly modifying your training-time #
# implementation of batch normalization, and inserting a line or two of #
# well-placed code. In particular, can you think of any matrix #
# transformations you could perform, that would enable you to copy over #
# the batch norm code and leave it almost unchanged? #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
attr_mean, attr_var = np.mean(x, axis=1).reshape(-1, 1), np.var(x, axis=1).reshape(-1, 1)
x_hat = (x - attr_mean) / np.sqrt(attr_var + eps)
out = x_hat * gamma + beta
cache = (x, gamma, x_hat, attr_mean, np.sqrt(attr_var+eps))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return out, cache
def layernorm_backward(dout, cache):
"""
Backward pass for layer normalization.
For this implementation, you can heavily rely on the work you've done already
for batch normalization.
Inputs:
- dout: Upstream derivatives, of shape (N, D)
- cache: Variable of intermediates from layernorm_forward.
Returns a tuple of:
- dx: Gradient with respect to inputs x, of shape (N, D)
- dgamma: Gradient with respect to scale parameter gamma, of shape (D,)
- dbeta: Gradient with respect to shift parameter beta, of shape (D,)
"""
dx, dgamma, dbeta = None, None, None
###########################################################################
# TODO: Implement the backward pass for layer norm. #
# #
# HINT: this can be done by slightly modifying your training-time #
# implementation of batch normalization. The hints to the forward pass #
# still apply! #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
x, gamma, x_hat, mu, std = cache
N, D = x.shape
dgamma = np.sum(dout * x_hat, axis=0)
dbeta = np.sum(dout, axis=0)
dx_hat = dout * gamma
dx_1 = dx_hat / std
dsigma = -0.5 * np.sum(dx_hat * (x - mu), axis=1).reshape(-1, 1) / (std ** 3)
dsigma_mu = -2/D * np.sum((x - mu), axis=1).reshape(-1, 1)
dmu = -np.sum(dx_hat / std, axis=1).reshape(-1, 1) + dsigma * dsigma_mu
dmu_x = 1 / D
dsigma_x = 2/D * (x - mu)
dx = dx_1 + dmu * dmu_x + dsigma * dsigma_x
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dgamma, dbeta
def dropout_forward(x, dropout_param):
"""
Performs the forward pass for (inverted) dropout.
Inputs:
- x: Input data, of any shape
- dropout_param: A dictionary with the following keys:
- p: Dropout parameter. We keep each neuron output with probability p.
- mode: 'test' or 'train'. If the mode is train, then perform dropout;
if the mode is test, then just return the input.
- seed: Seed for the random number generator. Passing seed makes this
function deterministic, which is needed for gradient checking but not
in real networks.
Outputs:
- out: Array of the same shape as x.
- cache: tuple (dropout_param, mask). In training mode, mask is the dropout
mask that was used to multiply the input; in test mode, mask is None.
NOTE: Please implement **inverted** dropout, not the vanilla version of dropout.
See http://cs231n.github.io/neural-networks-2/#reg for more details.
NOTE 2: Keep in mind that p is the probability of **keep** a neuron
output; this might be contrary to some sources, where it is referred to
as the probability of dropping a neuron output.
"""
p, mode = dropout_param['p'], dropout_param['mode']
if 'seed' in dropout_param:
np.random.seed(dropout_param['seed'])
mask = None
out = None
if mode == 'train':
#######################################################################
# TODO: 完成训练阶段的dropout正向传播。
# 将dropout掩码存储在mask变量中。
#######################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
D = x.shape[1]
mask = np.random.rand(1, D)
mask = np.where(mask < p, 1/p, 0)
out = x * mask
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#######################################################################
# END OF YOUR CODE #
#######################################################################
elif mode == 'test':
#######################################################################
# TODO: 完成测试阶段的dropout正向传播。
#######################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
out = x
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#######################################################################
# END OF YOUR CODE #
#######################################################################
cache = (dropout_param, mask)
out = out.astype(x.dtype, copy=False)
return out, cache
def dropout_backward(dout, cache):
"""
Perform the backward pass for (inverted) dropout.
Inputs:
- dout: Upstream derivatives, of any shape
- cache: (dropout_param, mask) from dropout_forward.
"""
dropout_param, mask = cache
mode = dropout_param['mode']
dx = None
if mode == 'train':
#######################################################################
# TODO: 完成训练阶段的dropout反向传播。
#######################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
dx = dout * mask
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#######################################################################
# END OF YOUR CODE #
#######################################################################
elif mode == 'test':
dx = dout
return dx
def conv_forward_naive(x, w, b, conv_param):
"""
A naive implementation of the forward pass for a convolutional layer.
The input consists of N data points, each with C channels, height H and
width W. We convolve each input with F different filters, where each filter
spans all C channels and has height HH and width WW.
Input:
- x: Input data of shape (N, C, H, W)
- w: Filter weights of shape (F, C, HH, WW)
- b: Biases, of shape (F,)
- conv_param: A dictionary with the following keys:
- 'stride': The number of pixels between adjacent receptive fields in the
horizontal and vertical directions.
- 'pad': The number of pixels that will be used to zero-pad the input.
During padding, 'pad' zeros should be placed symmetrically (i.e equally on both sides)
along the height and width axes of the input. Be careful not to modfiy the original
input x directly.
Returns a tuple of:
- out: Output data, of shape (N, F, H', W') where H' and W' are given by
H' = 1 + (H + 2 * pad - HH) / stride
W' = 1 + (W + 2 * pad - WW) / stride
- cache: (x, w, b, conv_param)
"""
out = None
###########################################################################
# TODO: 实现卷积正向传播。
# Hint: 你可以使用np.pad函数进行填充。
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
stride, pad = conv_param['stride'], conv_param['pad']
x_pad = np.pad(x, ((0,0),(0,0),(pad,pad),(pad,pad)), 'constant', constant_values = ((0,0),(0,0),(0,0),(0,0)))
out = []
N, C, H, W = x_pad.shape
F, C, HH, WW = w.shape
for i in range(N):
out_i = []
for j in range(F):
out_ij = [[np.sum(x_pad[i,:,hh:hh+HH,ww:ww+HH] * w[j,:])+b[j] for ww in range(0, W-WW+1, stride)] for hh in range(0, H-HH+1, stride)]
out_i.append(np.array(out_ij))
out.append(np.array(out_i))
out = np.array(out)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = (x, w, b, conv_param)
return out, cache
def conv_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a convolutional layer.
Inputs:
- dout: Upstream derivatives.
- cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive
Returns a tuple of:
- dx: Gradient with respect to x
- dw: Gradient with respect to w
- db: Gradient with respect to b
"""
dx, dw, db = None, None, None
###########################################################################
# TODO: 实现卷积的反向传播
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
x, w, b, conv_param = cache
stride, pad = conv_param['stride'], conv_param['pad']
N, C, H, W = x.shape
F, C, HH, WW = w.shape
N, F, Hp, Wp = dout.shape
x_pad = np.pad(x, ((0,0),(0,0),(pad,pad),(pad,pad)), 'constant', constant_values = ((0,0),(0,0),(0,0),(0,0)))
db = np.sum(dout, axis=(0,2,3))
dw = np.zeros(w.shape)
dx = np.zeros(x_pad.shape)
for i in range(F):
for j in range(C):
for m in range(HH):
for n in range(WW):
for t in range(N):
for ww in range(Wp):
for hh in range(Hp):
dw[i,j,m,n] += x_pad[t,j,hh*stride+m,ww*stride+n] * dout[t,i,hh,ww]
dx[t,j,hh*stride+m,ww*stride+n] += w[i,j,m,n] * dout[t,i,hh,ww]
dx = dx[:,:,pad:pad+H,pad:pad+W]
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
def max_pool_forward_naive(x, pool_param):
"""
A naive implementation of the forward pass for a max-pooling layer.
Inputs:
- x: Input data, of shape (N, C, H, W)
- pool_param: dictionary with the following keys:
- 'pool_height': The height of each pooling region
- 'pool_width': The width of each pooling region
- 'stride': The distance between adjacent pooling regions
No padding is necessary here. Output size is given by
Returns a tuple of:
- out: Output data, of shape (N, C, H', W') where H' and W' are given by
H' = 1 + (H - pool_height) / stride
W' = 1 + (W - pool_width) / stride
- cache: (x, pool_param)
"""
out = None
###########################################################################
# TODO: 完成最大池化的正向传播。 #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
N,C,H,W = x.shape
ph = pool_param['pool_height']
pw = pool_param['pool_width']
stride = pool_param['stride']
Hp = 1 + (H - ph) // stride
Wp = 1 + (W - pw) // stride
out = np.zeros((N,C,Hp,Wp))
for i in range(N):
for j in range(C):
for m in range(Hp):
for n in range(Wp):
out[i,j,m,n] += np.max(x[i,j,m*stride:m*stride+ph,n*stride:n*stride+pw])
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = (x, pool_param)
return out, cache
def max_pool_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a max-pooling layer.
Inputs:
- dout: Upstream derivatives
- cache: A tuple of (x, pool_param) as in the forward pass.
Returns:
- dx: Gradient with respect to x
"""
dx = None
###########################################################################
# TODO: 完成最大池化的反向传播 #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
x, pool_param = cache
N,C,H,W = x.shape
ph = pool_param['pool_height']
pw = pool_param['pool_width']
stride = pool_param['stride']
Hp = 1 + (H - ph) // stride
Wp = 1 + (W - pw) // stride
dx = np.zeros(x.shape)
for i in range(N):
for j in range(C):
for m in range(Hp):
for n in range(Wp):
xp = x[i,j,m*stride:m*stride+ph,n*stride:n*stride+pw]
idx = np.where(xp == np.max(xp))
dx[i,j,m*stride:m*stride+ph,n*stride:n*stride+pw][idx] += dout[i,j,m,n]
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
def spatial_batchnorm_forward(x, gamma, beta, bn_param):
"""
Computes the forward pass for spatial batch normalization.
Inputs:
- x: Input data of shape (N, C, H, W)
- gamma: Scale parameter, of shape (C,)
- beta: Shift parameter, of shape (C,)
- bn_param: Dictionary with the following keys:
- mode: 'train' or 'test'; required
- eps: Constant for numeric stability
- momentum: Constant for running mean / variance. momentum=0 means that
old information is discarded completely at every time step, while
momentum=1 means that new information is never incorporated. The
default of momentum=0.9 should work well in most situations.
- running_mean: Array of shape (D,) giving running mean of features
- running_var Array of shape (D,) giving running variance of features
Returns a tuple of:
- out: Output data, of shape (N, C, H, W)
- cache: Values needed for the backward pass
"""
out, cache = None, None
###########################################################################
# TODO: 完成空间批量归一化的正向传播。
#
# HINT: 您可以通过调用上面实现的批量标准化的原始版本来实现空间批量标准化。
# 您的实现应该非常简短；我们的代码少于五行。
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
N, C, H, W = x.shape
out, cache = batchnorm_forward(np.transpose(x, (0,2,3,1)).reshape(-1,C), gamma, beta, bn_param)
out = np.transpose(out.reshape(N, H, W, C), (0,3,1,2))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return out, cache
def spatial_batchnorm_backward(dout, cache):
"""
Computes the backward pass for spatial batch normalization.
Inputs:
- dout: Upstream derivatives, of shape (N, C, H, W)
- cache: Values from the forward pass
Returns a tuple of:
- dx: Gradient with respect to inputs, of shape (N, C, H, W)
- dgamma: Gradient with respect to scale parameter, of shape (C,)
- dbeta: Gradient with respect to shift parameter, of shape (C,)
"""
dx, dgamma, dbeta = None, None, None
###########################################################################
# TODO: 为空间批量归一化实现反向传递。
#
# HINT: 您可以通过调用上面实现的批量标准化的原始版本来实现空间批量标准化。
# 您的实现应该非常简短；我们的代码少于五行。
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
N, C, H, W = dout.shape
dx, dgamma, dbeta = batchnorm_backward_alt(np.transpose(dout, (0,2,3,1)).reshape(-1, C), cache)
dx = np.transpose(dx.reshape((N,H,W,C)), (0,3,1,2))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dgamma, dbeta
def spatial_groupnorm_forward(x, gamma, beta, G, gn_param):
"""
Computes the forward pass for spatial group normalization.
In contrast to layer normalization, group normalization splits each entry
in the data into G contiguous pieces, which it then normalizes independently.
Per feature shifting and scaling are then applied to the data, in a manner identical to that of batch normalization and layer normalization.
Inputs:
- x: Input data of shape (N, C, H, W)
- gamma: Scale parameter, of shape (C,)
- beta: Shift parameter, of shape (C,)
- G: Integer mumber of groups to split into, should be a divisor of C
- gn_param: Dictionary with the following keys:
- eps: Constant for numeric stability
Returns a tuple of:
- out: Output data, of shape (N, C, H, W)
- cache: Values needed for the backward pass
"""
out, cache = None, None
eps = gn_param.get('eps',1e-5)
###########################################################################
# TODO: 为空间组归一化实现正向传播。
# 这与层归一化的实现极为相似。
# 尤其要考虑如何转换矩阵，以使大部分代码与训练时批处理归一化和层归一化相似！
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
N, C, H, W = x.shape
x = np.transpose(x, (0,2,3,1)).reshape(-1, C)
g_size = C // G
out, cache = np.zeros(x.shape), []
for i in range(0, C, g_size):
l_out, l_cache = layernorm_forward(x[:,i:i+g_size], gamma.reshape(C)[i:i+g_size], beta.reshape(C)[i:i+g_size], gn_param)
out[:,i:i+g_size] = l_out
cache.append(l_cache)
out = np.transpose(out.reshape(N, H, W, C), (0,3,1,2))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return out, cache
def spatial_groupnorm_backward(dout, cache):
"""
Computes the backward pass for spatial group normalization.
Inputs:
- dout: Upstream derivatives, of shape (N, C, H, W)
- cache: Values from the forward pass
Returns a tuple of:
- dx: Gradient with respect to inputs, of shape (N, C, H, W)
- dgamma: Gradient with respect to scale parameter, of shape (C,)
- dbeta: Gradient with respect to shift parameter, of shape (C,)
"""
dx, dgamma, dbeta = None, None, None
###########################################################################
# TODO: 为空间组归一化实现反反向传播。
# 这将与层归一化的实现极为相似。
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
N, C, H, W = dout.shape
g_size = C // len(cache)
dout = np.transpose(dout, (0,2,3,1)).reshape(-1, C)
dx = np.zeros(dout.shape, dtype=float)
dgamma, dbeta = [], []
for i in range(0, C, g_size):
_dx, _dgamma, _dbeta = layernorm_backward(dout[:,i:i+g_size], cache[i//g_size])
dx[:,i:i+g_size] = _dx
dgamma.append(_dgamma)
dbeta.append(_dbeta)
dx = np.transpose(dx.reshape(N, H, W, C), (0,3,1,2))
dgamma = np.concatenate(tuple(dgamma), axis=0).reshape(1,C,1,1)
dbeta = np.concatenate(tuple(dbeta), axis=0).reshape(1,C,1,1)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dgamma, dbeta
def svm_loss(x, y):
"""
Computes the loss and gradient using for multiclass SVM classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth
class for the ith input.
- y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
0 <= y[i] < C
Returns a tuple of:
- loss: Scalar giving the loss
- dx: Gradient of the loss with respect to x
"""
N = x.shape[0]
correct_class_scores = x[np.arange(N), y]
margins = np.maximum(0, x - correct_class_scores[:, np.newaxis] + 1.0)
margins[np.arange(N), y] = 0
loss = np.sum(margins) / N
num_pos = np.sum(margins > 0, axis=1)
dx = np.zeros_like(x)
dx[margins > 0] = 1
dx[np.arange(N), y] -= num_pos
dx /= N
return loss, dx
def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth
class for the ith input.
- y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
0 <= y[i] < C
Returns a tuple of:
- loss: Scalar giving the loss
- dx: Gradient of the loss with respect to x
"""
shifted_logits = x - np.max(x, axis=1, keepdims=True)
Z = np.sum(np.exp(shifted_logits), axis=1, keepdims=True)
log_probs = shifted_logits - np.log(Z)
probs = np.exp(log_probs)
N = x.shape[0]
loss = -np.sum(log_probs[np.arange(N), y]) / N
dx = probs.copy()
dx[np.arange(N), y] -= 1
dx /= N
return loss, dx
daseCV/optim.py
import numpy as np
"""
This file implements various first-order update rules that are commonly used
for training neural networks. Each update rule accepts current weights and the
gradient of the loss with respect to those weights and produces the next set of
weights. Each update rule has the same interface:
def update(w, dw, config=None):
Inputs:
- w: A numpy array giving the current weights.
- dw: A numpy array of the same shape as w giving the gradient of the
loss with respect to w.
- config: A dictionary containing hyperparameter values such as learning
rate, momentum, etc. If the update rule requires caching values over many
iterations, then config will also hold these cached values.
Returns:
- next_w: The next point after the update.
- config: The config dictionary to be passed to the next iteration of the
update rule.
NOTE: For most update rules, the default learning rate will probably not
perform well; however the default values of the other hyperparameters should
work well for a variety of different problems.
For efficiency, update rules may perform in-place updates, mutating w and
setting next_w equal to w.
"""
def sgd(w, dw, config=None):
"""
Performs vanilla stochastic gradient descent.
config format:
- learning_rate: Scalar learning rate.
"""
if config is None: config = {}
config.setdefault('learning_rate', 1e-2)
w -= config['learning_rate'] * dw
return w, config
def sgd_momentum(w, dw, config=None):
"""
Performs stochastic gradient descent with momentum.
config format:
- learning_rate: Scalar learning rate.
- momentum: Scalar between 0 and 1 giving the momentum value.
Setting momentum = 0 reduces to sgd.
- velocity: A numpy array of the same shape as w and dw used to store a
moving average of the gradients.
"""
if config is None: config = {}
config.setdefault('learning_rate', 1e-2)
config.setdefault('momentum', 0.9)
v = config.get('velocity', np.zeros_like(w))
next_w = None
###########################################################################
# TODO: Implement the momentum update formula. Store the updated value in #
# the next_w variable. You should also use and update the velocity v. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
v = config['momentum'] * v - config['learning_rate'] * dw
next_w = w + v
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
config['velocity'] = v
return next_w, config
def rmsprop(w, dw, config=None):
"""
Uses the RMSProp update rule, which uses a moving average of squared
gradient values to set adaptive per-parameter learning rates.
config format:
- learning_rate: Scalar learning rate.
- decay_rate: Scalar between 0 and 1 giving the decay rate for the squared
gradient cache.
- epsilon: Small scalar used for smoothing to avoid dividing by zero.
- cache: Moving average of second moments of gradients.
"""
if config is None: config = {}
config.setdefault('learning_rate', 1e-2)
config.setdefault('decay_rate', 0.99)
config.setdefault('epsilon', 1e-8)
config.setdefault('cache', np.zeros_like(w))
next_w = None
###########################################################################
# TODO: Implement the RMSprop update formula, storing the next value of w #
# in the next_w variable. Don't forget to update cache value stored in #
# config['cache']. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
config['cache'] = config['decay_rate'] * config['cache'] + (1 - config['decay_rate']) * dw * dw
next_w = w - config['learning_rate'] * dw / (np.sqrt(config['cache'] + config['epsilon']))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return next_w, config
def adam(w, dw, config=None):
"""
Uses the Adam update rule, which incorporates moving averages of both the
gradient and its square and a bias correction term.
config format:
- learning_rate: Scalar learning rate.
- beta1: Decay rate for moving average of first moment of gradient.
- beta2: Decay rate for moving average of second moment of gradient.
- epsilon: Small scalar used for smoothing to avoid dividing by zero.
- m: Moving average of gradient.
- v: Moving average of squared gradient.
- t: Iteration number.
"""
if config is None: config = {}
config.setdefault('learning_rate', 1e-3)
config.setdefault('beta1', 0.9)
config.setdefault('beta2', 0.999)
config.setdefault('epsilon', 1e-8)
config.setdefault('m', np.zeros_like(w))
config.setdefault('v', np.zeros_like(w))
config.setdefault('t', 0)
next_w = None
###########################################################################
# TODO: Implement the Adam update formula, storing the next value of w in #
# the next_w variable. Don't forget to update the m, v, and t variables #
# stored in config. #
# #
# NOTE: In order to match the reference output, please modify t _before_ #
# using it in any calculations. #
###########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
config['t'] += 1
config['m'] = config['beta1'] * config['m'] + (1 - config['beta1']) * dw
m = config['m'] / (1 - config['beta1'] ** config['t'])
config['v'] = config['beta2'] * config['v'] + (1 - config['beta2']) * dw * dw
v = config['v'] / (1 - config['beta2'] ** config['t'])
next_w = w - config['learning_rate'] * m / (np.sqrt(v + config['epsilon']))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
###########################################################################
# END OF YOUR CODE #
###########################################################################
return next_w, config
daseCV/classifiers/cnn.py
from builtins import object
import numpy as np
from daseCV.layers import *
from daseCV.fast_layers import *
from daseCV.layer_utils import *
class ThreeLayerConvNet(object):
"""
A three-layer convolutional network with the following architecture:
conv - relu - 2x2 max pool - affine - relu - affine - softmax
The network operates on minibatches of data that have shape (N, C, H, W)
consisting of N images, each with height H and width W and with C input
channels.
"""
def __init__(self, input_dim=(3, 32, 32), num_filters=32, filter_size=7,
hidden_dim=100, num_classes=10, weight_scale=1e-3, reg=0.0,
dtype=np.float32):
"""
Initialize a new network.
Inputs:
- input_dim: Tuple (C, H, W) giving size of input data
- num_filters: Number of filters to use in the convolutional layer
- filter_size: Width/height of filters to use in the convolutional layer
- hidden_dim: Number of units to use in the fully-connected hidden layer
- num_classes: Number of scores to produce from the final affine layer.
- weight_scale: Scalar giving standard deviation for random initialization
of weights.
- reg: Scalar giving L2 regularization strength
- dtype: numpy datatype to use for computation.
"""
self.params = {}
self.reg = reg
self.dtype = dtype
############################################################################
# TODO: 初始化三层卷积网络的权重和偏差。
# 权重应用以0.0为中心的高斯初始化，标准差等于weight_scale；
# 偏差应初始化为零。所有权重和偏差应存储在字典self.params中。
# 使用键“ W1”和“ b1”存储卷积层的权重和偏差；使用键“ W2”和“ b2”
# 表示隐藏仿射层的权重和偏差，并使用键“ W3”和“ b3”表示输出仿射层的
# 权重和偏差。重要说明：对于本次作业，您可以假设第一个卷积层的padding和
# stride已经设置了，这样**输入的width和height就保留了**。看一下loss()
# 函数的前部分它是如何做的。
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
num_channels, H, W = input_dim
stride, pad = 1, (filter_size-1) // 2
pool_h, pool_w, pool_stride = 2, 2, 2
HH = 1 + (H + 2 * pad - filter_size) // stride
WW = 1 + (W + 2 * pad - filter_size) // stride
H_pool, W_pool = 1 + (HH - pool_h) // pool_stride, 1 + (WW - pool_h) // pool_stride
layer2_input_dim = num_filters * H_pool * W_pool
self.params['W1'] = np.random.normal(loc=0., scale=weight_scale, size=(num_filters, num_channels, filter_size, filter_size))
self.params['b1'] = np.zeros(num_filters)
self.params['W2'] = np.random.normal(loc=0., scale=weight_scale, size=(layer2_input_dim, hidden_dim))
self.params['b2'] = np.zeros(hidden_dim)
self.params['W3'] = np.random.normal(loc=0., scale=weight_scale, size=(hidden_dim, num_classes))
self.params['b3'] = np.zeros(num_classes)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
for k, v in self.params.items():
self.params[k] = v.astype(dtype)
def loss(self, X, y=None):
"""
Evaluate loss and gradient for the three-layer convolutional network.
Input / output: Same API as TwoLayerNet in fc_net.py.
"""
W1, b1 = self.params['W1'], self.params['b1']
W2, b2 = self.params['W2'], self.params['b2']
W3, b3 = self.params['W3'], self.params['b3']
# pass conv_param to the forward pass for the convolutional layer
# Padding and stride chosen to preserve the input spatial size
filter_size = W1.shape[2]
conv_param = {'stride': 1, 'pad': (filter_size - 1) // 2}
# pass pool_param to the forward pass for the max-pooling layer
pool_param = {'pool_height': 2, 'pool_width': 2, 'stride': 2}
scores = None
############################################################################
# TODO: 实现三层卷积网络的正向传播，计算X的每类的分数并将其存储在scores变量中。
#请注意，您可以在实现中使用daseCV/fast_layers.py和daseCV/layer_utils.py中定义的功能（已导入）。
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
conv_out, conv_cache = conv_relu_pool_forward(X, W1, b1, conv_param, pool_param)
# conv_shape = conv_out.shape
# conv_out = conv_out.reshape(conv_out.shape[0], W2.shape[0])
layer2_out, layer2_cache = affine_relu_forward(conv_out, W2, b2)
scores, scores_cache = affine_forward(layer2_out, W3, b3)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
if y is None:
return scores
loss, grads = 0, {}
############################################################################
# TODO: 完成三层卷积网络的反向传播，将损失和梯度存储在变量loss和grads中。
# 使用softmax计算损失，并使用grads[k]保存self.params[k]的梯度。不要忘记增加L2正则化！
#
# NOTE: 为确保您的实现与我们的实现相同并通过自动化测试，请确保您的L2正则化系数为0.5，
# 以简化梯度的表达式。
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
loss, dout = softmax_loss(scores, y)
reg_sum = np.sum(W1 ** 2) + np.sum(W2 ** 2) + np.sum(W3 ** 2)
reg_sum *= 0.5 * self.reg
loss += reg_sum
dout, grads['W3'], grads['b3'] = affine_backward(dout, scores_cache)
dout, grads['W2'], grads['b2'] = affine_relu_backward(dout, layer2_cache)
dout, grads['W1'], grads['b1'] = conv_relu_pool_backward(dout, conv_cache)
grads['W1'] += self.reg * W1
grads['W2'] += self.reg * W2
grads['W3'] += self.reg * W3
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
daseCV/classifiers/fc_net.py
from builtins import range
from builtins import object
import numpy as np
from daseCV.layers import *
from daseCV.layer_utils import *
class TwoLayerNet(object):
"""
采用模块化设计实现具有ReLU和softmax损失函数的两层全连接神经网络。
假设D是输入维度，H是隐藏层维度，一共有C类标签。
网络架构应该是：affine - relu - affine - softmax.
注意，这个类不实现梯度下降；它将与负责优化的Solver对象进行交互。
模型的可学习参数存储在字典self.params中。键是参数名称，值是numpy数组。
"""
def __init__(self, input_dim=3*32*32, hidden_dim=100, num_classes=10,
weight_scale=1e-3, reg=0.0):
"""
Initialize a new network.
Inputs:
- input_dim: An integer giving the size of the input
- hidden_dim: An integer giving the size of the hidden layer
- num_classes: An integer giving the number of classes to classify
- weight_scale: Scalar giving the standard deviation for random
initialization of the weights.
- reg: Scalar giving L2 regularization strength.
"""
self.params = {}
self.reg = reg
############################################################################
# TODO: Initialize the weights and biases of the two-layer net. Weights #
# should be initialized from a Gaussian centered at 0.0 with #
# standard deviation equal to weight_scale, and biases should be #
# initialized to zero. All weights and biases should be stored in the #
# dictionary self.params, with first layer weights #
# and biases using the keys 'W1' and 'b1' and second layer #
# weights and biases using the keys 'W2' and 'b2'. #
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
self.params['W1'] = np.random.normal(0, weight_scale, (input_dim, hidden_dim))
self.params['W2'] = np.random.normal(0, weight_scale, (hidden_dim, num_classes))
self.params['b1'] = np.zeros((hidden_dim))
self.params['b2'] = np.zeros((num_classes))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
def loss(self, X, y=None):
"""
对小批量数据计算损失和梯度
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. #
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
out1, cache1 = affine_forward(X, self.params['W1'], self.params['b1'])
out2, cache2 = relu_forward(out1)
scores, cache3 = affine_forward(out2, self.params['W2'], self.params['b2'])
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# 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. #
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
loss, dout = softmax_loss(scores, y)
loss += 0.5 * self.reg * (np.sum(self.params['W1']*self.params['W1']) + np.sum(self.params['W2']*self.params['W2']))
dout2, grads['W2'], grads['b2'] = affine_backward(dout, cache3)
dout1 = relu_backward(dout2, cache2)
dX, grads['W1'], grads['b1'] = affine_backward(dout1, cache1)
grads['W1'] += self.reg * self.params['W1']
grads['W2'] += self.reg * self.params['W2']
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
class FullyConnectedNet(object):
"""
一个任意隐藏层数和神经元数的全连接神经网络，其中 ReLU 激活函数，sofmax 损失函数，同时可选的
采用 dropout 和 batch normalization(批量归一化)。那么，对于一个L层的神经网络来说，其框架是：
{affine ‐ [batch norm] ‐ relu ‐ [dropout]} x (L ‐ 1) ‐ affine ‐ softmax
其中的[batch norm]和[dropout]是可选非必须的，框架中{...}部分将会重复L‐1次，代表L‐1 个隐藏层。
与我们在上面定义的 TwoLayerNet() 类保持一致，所有待学习的参数都会存在self.params 字典中，
并且最终会被最优化 Solver() 类训练学习得到。
"""
def __init__(self, hidden_dims, input_dim=3*32*32, num_classes=10,
dropout=1, normalization=None, reg=0.0,
weight_scale=1e-2, dtype=np.float32, seed=None):
"""
Initialize a new FullyConnectedNet.
Inputs:
- hidden_dims: A list of integers giving the size of each hidden layer.
- input_dim: An integer giving the size of the input.
- num_classes: An integer giving the number of classes to classify.
- dropout: Scalar between 0 and 1 giving dropout strength. If dropout=1 then
the network should not use dropout at all.
- normalization: What type of normalization the network should use. Valid values
are "batchnorm", "layernorm", or None for no normalization (the default).
- reg: Scalar giving L2 regularization strength.
- weight_scale: Scalar giving the standard deviation for random
initialization of the weights.
- dtype: A numpy datatype object; all computations will be performed using
this datatype. float32 is faster but less accurate, so you should use
float64 for numeric gradient checking.
- seed: If not None, then pass this random seed to the dropout layers. This
will make the dropout layers deteriminstic so we can gradient check the
model.
"""
self.normalization = normalization
self.use_dropout = dropout != 1
self.reg = reg
self.num_layers = 1 + len(hidden_dims)
self.dtype = dtype
self.params = {}
############################################################################
# TODO: Initialize the parameters of the network, storing all values in #
# the self.params dictionary. Store weights and biases for the first layer #
# in W1 and b1; for the second layer use W2 and b2, etc. Weights should be #
# initialized from a normal distribution centered at 0 with standard #
# deviation equal to weight_scale. Biases should be initialized to zero. #
# #
# When using batch normalization, store scale and shift parameters for the #
# first layer in gamma1 and beta1; for the second layer use gamma2 and #
# beta2, etc. Scale parameters should be initialized to ones and shift #
# parameters should be initialized to zeros. #
############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
L_input_dim = input_dim
for i, hd in enumerate(hidden_dims):
W_name, b_name = 'W%d'%(i+1), 'b%d'%(i+1)
self.params[W_name] = weight_scale * np.random.randn(L_input_dim, hd)
self.params[b_name] = np.zeros(hd)
if self.normalization != None:
gamma_name, beta_name = 'gamma%d'%(i+1), 'beta%d'%(i+1)
self.params[gamma_name] = np.ones(hd)
self.params[beta_name] = np.zeros(hd)
L_input_dim = hd
self.params['W%d'%(self.num_layers)] = weight_scale * np.random.randn(L_input_dim, num_classes)
self.params['b%d'%(self.num_layers)] = np.zeros(num_classes)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
# When using dropout we need to pass a dropout_param dictionary to each
# dropout layer so that the layer knows the dropout probability and the mode
# (train / test). You can pass the same dropout_param to each dropout layer.
self.dropout_param = {}
if self.use_dropout:
self.dropout_param = {'mode': 'train', 'p': dropout}
if seed is not None:
self.dropout_param['seed'] = seed
# With batch normalization we need to keep track of running means and
# variances, so we need to pass a special bn_param object to each batch
# normalization layer. You should pass self.bn_params[0] to the forward pass
# of the first batch normalization layer, self.bn_params[1] to the forward
# pass of the second batch normalization layer, etc.
self.bn_params = []
if self.normalization=='batchnorm':
self.bn_params = [{'mode': 'train'} for i in range(self.num_layers - 1)]
if self.normalization=='layernorm':
self.bn_params = [{} for i in range(self.num_layers - 1)]
# Cast all parameters to the correct datatype
for k, v in self.params.items():
self.params[k] = v.astype(dtype)
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)*****
if self.normalization == None:
f_forward, f_backward = affine_relu_forward, affine_relu_backward
elif self.normalization == 'batchnorm':
f_forward, f_backward = affine_bn_relu_forward, affine_bn_relu_backward
elif self.normalization == 'layernorm':
f_forward, f_backward = affine_ln_relu_forward, affine_ln_relu_backward
else:
raise ValueError('Normalization error:', self.normalization)
L_input = X
out_cache = [None] * self.num_layers
drop_cache = [None] * (self.num_layers-1)
for i in range(0, self.num_layers-1):
W_name, b_name = 'W%d'%(i+1), 'b%d'%(i+1)
if self.normalization != None:
gamma_name, beta_name = 'gamma%d'%(i+1), 'beta%d'%(i+1)
L_input, out_cache[i] = f_forward(L_input, self.params[W_name], self.params[b_name], self.params[gamma_name], self.params[beta_name], self.bn_params[i])
else:
L_input, out_cache[i] = f_forward(L_input, self.params[W_name], self.params[b_name])
if self.use_dropout:
L_input, drop_cache[i] = dropout_forward(L_input, self.dropout_param)
scores, out_cache[-1] = affine_forward(L_input, self.params['W%d'%(self.num_layers)], self.params['b%d'%(self.num_layers)])
# *****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)
reg_sum = 0.
for i in range(self.num_layers):
W_name = 'W' + str(i+1)
reg_sum += np.sum(self.params[W_name] * self.params[W_name])
loss += 0.5 * self.reg * reg_sum
for i in range(self.num_layers, 0, -1):
W_name, b_name = 'W'+str(i), 'b'+str(i)
if i == self.num_layers:
dout, grads[W_name], grads[b_name] = affine_backward(dout, out_cache[i-1])
else:
if self.use_dropout:
dout = dropout_backward(dout, drop_cache[i-1])
if self.normalization != None:
gamma_name, beta_name = 'gamma'+str(i), 'beta'+str(i)
dout, grads[W_name], grads[b_name], grads[gamma_name], grads[beta_name] = f_backward(dout, out_cache[i-1])
else:
dout, grads[W_name], grads[b_name] = f_backward(dout, out_cache[i-1])
grads[W_name] += self.reg * self.params[W_name]
del out_cache, drop_cache
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads