话不多说，直接上代码：
Convolution: Naive forward pass
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: Implement the convolutional forward pass. #
# Hint: you can use the function np.pad for padding. #
###########################################################################
N, C, H, W = x.shape
F, _, HH, WW = w.shape
stride, pad = conv_param['stride'], conv_param['pad']
H_out = int(1 + (H + 2 * pad - HH) / stride)
W_out = int(1 + (W + 2 * pad - WW) / stride)
out = np.zeros((N, F, H_out, W_out)) #预分配输出out的内存
x_pad = np.pad(x, ((0,), (0,), (pad,), (pad,)), mode='constant', constant_values=0)
for i in range(H_out):
for j in range(W_out):
#逐一计算输出值
x_pad_mask = x_pad[:, :, stride * i:HH + stride * i, stride * j: stride * j + WW]
for k in range(F):
out[:, k, i, j] = np.sum(x_pad_mask * w[k, :, :, :], axis=(1,2,3))
out += b[None, :, None, None] #加上偏置，这里None添加了维度，使得能够正确相加
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = (x, w, b, conv_param)
return out, cache
Convolution: Naive backward pass
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: Implement the convolutional backward pass. #
###########################################################################
x, w, b, conv_param = cache
N, C, H, W = x.shape
F, _, HH, WW = w.shape
stride, pad = conv_param['stride'], conv_param['pad']
H_out = int(1 + (H + 2 * pad - HH) / stride)
W_out = int(1 + (W + 2 * pad - WW) / stride)
x_pad = np.pad(x, ((0,), (0,), (pad,), (pad,)), mode='constant', constant_values=0)
dx = np.zeros_like(x)
dx_pad = np.zeros_like(x_pad)
dw = np.zeros_like(w)
db = np.sum(dout, axis=(0,2,3))
for i in range(H_out):
for j in range(W_out):
x_pad_masked = x_pad[:, :, i*stride:i*stride+HH, j*stride:j*stride+WW]
# 注意弄清输出的每一位，有哪些输入X和W参与，逐一计算梯度
for k in range(F):
dw[k ,: ,: ,:] += np.sum(x_pad_masked * (dout[:, k, i, j])[:, None, None, None], axis=0)
for n in range(N):
dx_pad[n, :, i*stride:i*stride+HH, j*stride:j*stride+WW] += np.sum((w[:, :, :, :] *
(dout[n, :, i, j])[:,None ,None, None]), axis=0)
dx = dx_pad[:,:,pad:-pad,pad:-pad]
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
测试结果
Testing conv_backward_naive function
dx error: 1.159803161159293e-08
dw error: 2.247109434939654e-10
db error: 3.37264006649648e-11
max_pool
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: Implement the max-pooling forward pass #
###########################################################################
HH, WW, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride']
N, C, H, W = x.shape
H_out = int(1 + (H - HH) / stride)
W_out = int(1 + (W - WW) / stride)
out = np.zeros((N, C, H_out, W_out))
for i in range(H_out):
for j in range(W_out):
x_mask = x[:, :, stride * i:stride * i + HH, stride * j:stride * j + WW]
out[:, :, i, j] = np.max(x_mask, axis=(2, 3))
###########################################################################
# 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: Implement the max-pooling backward pass #
###########################################################################
x, pool_param = cache
N, C, H, W = x.shape
HH, WW, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride']
H_out = int((H-HH)/stride+1)
W_out = int((W-WW)/stride+1)
dx = np.zeros_like(x)
for i in range(H_out):
for j in range(W_out):
x_masked = x[:,:,i*stride : i*stride+HH, j*stride : j*stride+WW]
max_x_masked = np.max(x_masked,axis=(2,3))
temp_binary_mask = (x_masked == (max_x_masked)[:,:,None,None])
dx[:,:,i*stride : i*stride+HH, j*stride : j*stride+WW] += temp_binary_mask * (dout[:,:,i,j])[:,:,None,None]
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
Three-layer ConvNet
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: Initialize weights and biases for the three-layer convolutional #
# network. Weights should be initialized from a Gaussian centered at 0.0 #
# with standard deviation equal to weight_scale; biases should be #
# initialized to zero. All weights and biases should be stored in the #
# dictionary self.params. Store weights and biases for the convolutional #
# layer using the keys 'W1' and 'b1'; use keys 'W2' and 'b2' for the #
# weights and biases of the hidden affine layer, and keys 'W3' and 'b3' #
# for the weights and biases of the output affine layer. #
# #
# IMPORTANT: For this assignment, you can assume that the padding #
# and stride of the first convolutional layer are chosen so that #
# **the width and height of the input are preserved**. Take a look at #
# the start of the loss() function to see how that happens. #
############################################################################
C, H, W = input_dim
self.params['W1'] = np.random.normal(0, weight_scale, (num_filters, C, filter_size, filter_size))
self.params['b1'] = np.zeros((num_filters))
self.params['W2'] = np.random.normal(0, weight_scale, (int((H / 2) * (W / 2) * num_filters), hidden_dim))
self.params['b2'] = np.zeros(hidden_dim)
self.params['W3'] = np.random.normal(0, weight_scale, (hidden_dim, num_classes))
self.params['b3'] = np.zeros(num_classes)
############################################################################
# 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: Implement the forward pass for the three-layer convolutional net, #
# computing the class scores for X and storing them in the scores #
# variable. #
# #
# Remember you can use the functions defined in cs231n/fast_layers.py and #
# cs231n/layer_utils.py in your implementation (already imported). #
############################################################################
out_conv, cache_conv = conv_relu_pool_forward(X, W1, b1, conv_param, pool_param)
out_fc1, cache_fc1 = affine_relu_forward(out_conv, W2, b2)
scores, cache_fc2 = affine_forward(out_fc1, W3, b3)
############################################################################
# END OF YOUR CODE #
############################################################################
if y is None:
return scores
loss, grads = 0, {}
############################################################################
# TODO: Implement the backward pass for the three-layer convolutional net, #
# storing the loss and gradients in the loss and grads variables. 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, dout = softmax_loss(scores, y)
loss += 0.5 * self.reg * (np.sum(W1**2) + np.sum(W2**2) + np.sum(W3**2))
dx3, dw3, db3 = affine_backward(dout, cache_fc2)
grads['W3'] = dw3 + self.reg * W3
grads['b3'] = db3
dx2, dw2, db2 = affine_relu_backward(dx3, cache_fc1)
grads['W2'] = dw2 + self.reg * W2
grads['b2'] = db2
dx1, dw1, db1 = conv_relu_pool_backward(dx2, cache_conv)
grads['W1'] = dw1 + self.reg * W1
grads['b1'] = db1
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
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