cs231-assignment2-总结-代码
cs231-assignment2-总结
- 技巧
技巧
- dx是和x形状一样全为0的矩阵，将dx里x>0的位置设为1
dx = np.zeros_like(x, dtype=float)
dx[x > 0] = 1
- 把dx的形状变成x的形状
dx = np.reshape(dx, x.shape)
- batch norm是对特征值归一化，不是对图像归一化
- 计算出来的梯度先化简后再写成代码减少计算量
x_norm, gamma, beta, sample_mean, sample_var, x, eps = cache
dnorm = gamma * dout
dvar = -0.5 * np.sum(dnorm * (x - sample_mean), axis=0) * np.power(sample_var + eps, -3/2)
dmean = -1 * np.sum(dnorm * np.power(sample_var + eps, -1/2), axis=0) - 2 * dvar * np.mean(x - sample_mean, axis=0)
dgamma = np.sum(dout * x_norm, axis=0)
dbeta = np.sum(dout)
- mask
mask = np.random.rand(*x.shape) < p
- np的补零操作
x_padded = np.pad(x, ((0, 0), (0, 0), (pad, pad), (pad, pad)), mode='constant')
- 卷积网络的input 有N个batch output也会有N个
Input:
- x: Input data of shape (N, C, H, W)
- w: Filter weights of shape (F, C, HH, WW)
- b: Biases, of shape (F,)
Output:
- 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
- 让最大的值为1，其余为0
m = np.max(win)
(m== win)
- 拼接的效果
layers_dims = [input_dim] + hidden_dims + [num_classes]
-
为什么要用平滑平均：
在assignment1里，train和test都使用的是整体train集的平均，这里采用用了平滑平均。
https://www.zhihu.com/question/55621104 -
顺序：
wx+b - batch norm - relu - dropout
code：
layers.py
import numpy as np
def affine_forward(x, w, b):
out = None
N = x.shape[0]
x_reshape = x.reshape(N, -1)
out = np.dot(x_reshape, w) + b
cache = (x, w, b)
return out, cache
def affine_backward(dout, cache):
"""
Computes the backward pass for an affine layer.
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)
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
N, M = dout.shape
x_reshape = x.reshape(N, -1)
dw = np.transpose(x_reshape).dot(dout)
dx_reshape = dout.dot(np.transpose(dw))
dx = np.reshape(dx_reshape, x.shape)
db = np.sum(dout, axis=0, keepdims=True)
return dx, dw, db
def relu_forward(x):
"""
Computes the forward pass for a layer of rectified linear units (ReLUs).
Input:
- x: Inputs, of any shape
Returns a tuple of:
- out: Output, of the same shape as x
- cache: x
"""
out = None
out = np.maximum(x, 0)
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
dx = dout
dx[x <= 0] = 0
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':
sample_mean = np.mean(x, axis=0, keepdims=True)
sample_var = np.var(x, axis=0, keepdims=True)
x_norm = (x - sample_mean)/np.sqrt(sample_var + eps)
out = gamma * x_norm + beta
cache = (x_normalized, gamma, beta, sample_mean, sample_var, x, eps)
running_mean = momentum * running_mean + (1 - momentum) * sample_mean
running_var = momentum * running_var + (1 - momentum) * sample_var
elif mode == 'test':
x_norm = (x - sample_mean) / np.sqrt(sample_var + eps)
out = gamma * x_norm + beta
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
N, D = x.shape
x_norm, gamma, beta, sample_mean, sample_var, x, eps = cache
dnorm = gamma * dout
dvar = -0.5 * np.sum(dnorm * (x - sample_mean), axis=0) * np.power(sample_var + eps, -3/2)
dmean = -1.0 * np.sum(dnorm * np.power(sample_var + eps, -1/2), axis=0) - 2.0 * dvar * np.mean(x - sample_mean, axis=0)
dgamma = np.sum(dout * x_norm, axis=0)
dbeta = np.sum(dout, axis=0)
dx = dnorm * np.power(sample_var + eps, -1/2) + 2.0/N * dnorm * (x - sample_mean) + 1.0 * dmean/N
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.
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
x_normalized, gamma, beta, sample_mean, sample_var, x, eps = cache
N, D = x.shape
dx_normalized = dout * gamma # [N,D]
x_mu = x - sample_mean # [N,D]
sample_std_inv = 1.0 / np.sqrt(sample_var + eps) # [1,D]
dsample_var = -0.5 * np.sum(dx_normalized * x_mu, axis=0, keepdims=True) * sample_std_inv ** 3
dsample_mean = -1.0 * np.sum(dx_normalized * sample_std_inv, axis=0, keepdims=True) - \
2.0 * dsample_var * np.mean(x_mu, axis=0, keepdims=True)
dx1 = dx_normalized * sample_std_inv
dx2 = 2.0 / N * dsample_var * x_mu
dx = dx1 + dx2 + 1.0 / N * dsample_mean
dgamma = np.sum(dout * x_normalized, axis=0, keepdims=True)
dbeta = np.sum(dout, axis=0, keepdims=True)
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 drop 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: A 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.
"""
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':
mask = np.random.rand(*x.shape) < p / p
out = x * mask
elif mode == 'test':
out = x
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':
dx = dout * mask
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 HH.
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.
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
stride = conv_param['stride']
pad = conv_param['pad']
N, C, H, W = x.shape
F, C, HH, WW = w.shape
x_padded = np.pad(x, ((0, 0), (0, 0), (pad, pad), (pad, pad)), mode='constant')
H_new = 1 + (H + 2 * pad - HH) / stride
W_new = 1 + (W + 2 * pad - WW) / stride
out = np.zeros((N, F, H_new, W_new))
for i in xrange(N): # ith image
for f in xrange(F): # fth filter
for j in xrange(H_new):
for k in xrange(W_new):
out[i, f, j, k] = np.sum(x_padded[i, :, j*stride: j*stride+HH, k*stride: k*stride+WW] * w[f]) + b[f]
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
x, w, b, conv_param = cache
N, C, H, W = x.shape
F, C, HH, WW = w.shape
pad = conv_param['pad']
stride = conv_param['stride']
H_new = 1 + (H + 2 * pad - HH) / stride
W_new = 1 + (W + 2 * pad - WW) / stride
N, C, H, W = x.shape
F, C, HH, WW = w.shape
x_padded = np.pad(x, ((0, 0), (0, 0), (pad, pad), (pad, pad)), mode='constant')
dx_padded = np.zeros_like(x_padded, dtype = float)
dx = np.zeros_like(x, dtype=float)
dw = np.zeros_like(w, dtype=float)
db = np.zeros_like(b, dtype=float)
for i in xrange(N): # ith image
for f in xrange(F): # fth filter
for j in xrange(H_new):
for k in xrange(W_new):
dx_padded[i, :, j*stride: j*stride+HH, k*stride: k*stride+WW] += dout[i, f, j ,k] * w[f]
dw[f] += dout[i, f, j, k] * x_padded[i, :, j*stride: j*stride+HH, k*stride: k*stride+WW]
db[f] += dout[i, f, j, k]
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
Returns a tuple of:
- out: Output data
- cache: (x, pool_param)
"""
out = None
N, C, H, W = np.shape(x)
pool_height, pool_width, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride']
H_new = 1 + (H - pool_height) / stride
W_new = 1 + (W - pool_width) / stride
out = np.zeros((N, C, H_new, W_new))
for i in xrange(N): # ith image
for f in xrange(C): # fth filter
for j in xrange(H_new):
for k in xrange(W_new):
out[i, f, j, k] = np.max(x[i, f, j*stride: j*stride+pool_height, k*stride: k*stride+pool_width])
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
x, pool_param = cache
N, C, H, W = np.shape(x)
pool_height, pool_width, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride']
H_new = 1 + (H - pool_height) / stride
W_new = 1 + (W - pool_width) / stride
dx = np.zeros_like(x)
for i in xrange(N): # ith image
for f in xrange(C): # fth filter
for j in xrange(H_new):
for k in xrange(W_new):
win = x[i, f, j * stride: j * stride + pool_height, k * stride: k * stride + pool_width]
m = np.max(win)
dx[i, f, j * stride: j * stride + pool_height, k * stride: k * stride + pool_width] += (m== win) * dout[i, f, j, k]
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
N, C, H, W = x.shape
x_new = x.transpose(0, 2, 3, 1).reshape(N*H*W, C)
out_new, cache = batchnorm_forward(x_new, gamma, beta, bn_param)
out = out_new.reshape(N, H, W, C).transpose(0, 3, 1, 2)
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
N, C, H, W = dout.shape
dout_new = dout.transpose(0, 2, 3, 1).reshape(N * H * W, C)
dx_new, dgamma, dbeta = batchnorm_backward(dout_new, cache)
dx = dx_new.reshape(N, H, W, C).transpose(0, 3, 1, 2)
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
"""
probs = np.exp(x - np.max(x, axis=1, keepdims=True))
probs /= np.sum(probs, axis=1, keepdims=True)
N = x.shape[0]
loss = -np.sum(np.log(probs[np.arange(N), y])) / N
dx = probs.copy()
dx[np.arange(N), y] -= 1
dx /= N
return loss, dx
layer_utils.py: 多个层合并
fast_layers.py： 优化卷积层，不需要循环
solver.py：优化的顶层
optim.py：优化的模块
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. #
#############################################################################
v = config['momentum'] * v - config['learning_rate'] * dw
next_w = w + v
#############################################################################
# END OF YOUR CODE #
#############################################################################
config['velocity'] = v
return next_w, config
def rmsprop(x, dx, 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(x))
next_x = None
#############################################################################
# TODO: Implement the RMSprop update formula, storing the next value of x #
# in the next_x variable. Don't forget to update cache value stored in #
# config['cache']. #
#############################################################################
config['cache'] = config['decay_rate'] * config['cache'] + (1 - config['decay_rate']) * (dx**2)
next_x = x - config['learning_rate'] * dx / (np.sqrt(config['cache']) + config['epsilon'])
#############################################################################
# END OF YOUR CODE #
#############################################################################
return next_x, config
def adam(x, dx, 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(x))
config.setdefault('v', np.zeros_like(x))
config.setdefault('t', 0)
next_x = None
#############################################################################
# TODO: Implement the Adam update formula, storing the next value of x in #
# the next_x variable. Don't forget to update the m, v, and t variables #
# stored in config. #
#############################################################################
m = config['m']
beta1 = config['beta1']
beta2 = config['beta2']
eps = config['epsilon']
v = config['v']
learning_rate = config['learning_rate']
config['t'] += 1
m = beta1 * m + (1 - beta1) * dx
v = beta2 * v + (1 - beta2) * (dx ** 2)
m_bias = m / (1 - beta1 ** t)
v_bias = v / (1 - beta2 ** t)
next_x = x - learning_rate * m_bias / (np.sqrt(v_bias) + eps)
config['m'] = m
config['v'] = v
#############################################################################
# END OF YOUR CODE #
#############################################################################
return next_x, config
fc_net.py: 全连接层的顶层设计
import numpy as np
from layers import *
from layer_utils import *
class TwoLayerNet(object):
"""
A two-layer fully-connected neural network with ReLU nonlinearity and
softmax loss that uses a modular layer design. We assume an input dimension
of D, a hidden dimension of H, and perform classification over C classes.
The architecure should be affine - relu - affine - softmax.
Note that this class does not implement gradient descent; instead, it
will interact with a separate Solver object that is responsible for running
optimization.
The learnable parameters of the model are stored in the dictionary
self.params that maps parameter names to numpy arrays.
"""
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
- dropout: Scalar between 0 and 1 giving dropout strength.
- 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 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'. #
############################################################################
self.params['W1'] = weight_scale * np.random.randn(input_dim, hidden_dim)
self.params['b1'] = np.zeros((1, hidden_dim))
self.params['W2'] = weight_scale * np.random.randn(hidden_dim, num_classes)
self.params['b2'] = np.zeros((1, num_classes))
############################################################################
# END OF YOUR CODE #
############################################################################
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
W1, b1 = self.params['W1'], self.params['b1']
W2, b2 = self.params['W2'], self.params['b2']
N = X.shape[0]
h1, cache1 = affine_relu_forward(X, W1, b1)
out, cache2 = affine_forward(h1, W2, b2)
scores = out # (N,C)
# If y is None then we are in test mode so just return scores
if y is None:
return scores
loss, grads = 0, {}
data_loss, dscores = softmax_loss(scores, y)
reg_loss = 0.5 * self.reg * np.sum(W1 * W1) + 0.5 * self.reg * np.sum(W2 * W2)
loss = data_loss + reg_loss
# Backward pass: compute gradients
dh1, dW2, db2 = affine_backward(dscores, cache2)
dX, dW1, db1 = affine_relu_backward(dh1, cache1)
# Add the regularization gradient contribution
dW2 += self.reg * W2
dW1 += self.reg * W1
grads['W1'] = dW1
grads['b1'] = db1
grads['W2'] = dW2
grads['b2'] = db2
return loss, grads
class FullyConnectedNet(object):
"""
A fully-connected neural network with an arbitrary number of hidden layers,
ReLU nonlinearities, and a softmax loss function. This will also implement
dropout and batch normalization as options. For a network with L layers,
the architecture will be
{affine - [batch norm] - relu - [dropout]} x (L - 1) - affine - softmax
where batch normalization and dropout are optional, and the {...} block is
repeated L - 1 times.
Similar to the TwoLayerNet above, learnable parameters are stored in the
self.params dictionary and will be learned using the Solver class.
"""
def __init__(self, hidden_dims, input_dim=3*32*32, num_classes=10,
dropout=0, use_batchnorm=False, 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=0 then
the network should not use dropout at all.
- use_batchnorm: Whether or not the network should use batch normalization.
- 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.use_batchnorm = use_batchnorm
self.use_dropout = dropout > 0
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 with standard deviation equal to #
# weight_scale and 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 one and shift #
# parameters should be initialized to zero. #
############################################################################
layers_dims = [input_dim] + hidden_dims + [num_classes]
for i in range(self.num_layers):
self.params['W'+str(i+1)] = weight_scale * np.random.randn(layers_dims[i], layers_dims[i+1])
self.params['b' + str(i + 1)] = np.zeros(1, layers_dims[i+1], dtype=dtype)
if self.use_batchnorm and i < len(hidden_dims):
self.params['gamma' + str(i + 1)] = np.ones(1, layers_dims[i+1], dtype=dtype)
self.params['beta' + str(i + 1)] = np.zeros(1, layers_dims[i+1], dtype=dtype)
############################################################################
# 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.use_batchnorm:
self.bn_params = [{'mode': 'train'} for i in xrange(self.num_layers - 1)]
# Cast all parameters to the correct datatype
for k, v in self.params.iteritems():
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.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. #
############################################################################
h, cache1, cache2, cache3, cache4, bn, out = {}, {}, {}, {}, {}, {}, {}
out[0] = X
for i in range(self.num_layers-2):
W, b = self.params['W' + str(i + 1)], self.params['b'+str(i+1)]
if self.use_batcnorm:
gamma, beta = self.params['gamma' + str(i + 1)], self.params['beta' + str(i + 1)]
h[i], cache1[i] = affine_forward(out[i], W, b)
bn[i], cache2[i] = batchnorm_forward(h[i], gamma, beta, bn_params)
out[i+1], cache3[i] = relu_forward(bn[i])
if self.use_dropout:
out[i+1], cache4[i] = dropout_forward(out[i+1], self.dropout_param)
else:
out[i+1], cache3[i] = affine_relu_forward(out[i], W, b)
if self.use_dropout:
out[i+1], cache4[i] = dropout_forward(out[i+1], self.dropout_param)
W, b = self.params['W' + str(self.num_layers)], self.params['b' + str(self.num_layers)]
scores, cache = affine_forward(out[self.num_layers-1], 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 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. #
############################################################################
data_loss, dscores = softmax_loss(scores, y)
reg_loss = 0
for i in range(self.num_layers):
W = self.params['W' + str(i + 1)]
reg_loss += 0.5 * self.reg * (np.sum(np.square(W)))
loss = data_loss + reg_loss
dout, dbn, dh, ddrop = {}, {}, {}, {}
t = self.num_layers - 1
dout[t], grad['W'+str(t+1)], grad['b'+str(t+1)] = affine_backward(dscores, cache)
for i in range(t):
if self.use_batcnorm:
if self.use_dropout:
dout[t-i] = dropout_backward(dout[t-i], cache4[t-1-i])
bn[t-1-i] = relu_backward(dout[t-i], cache3[t-1-i])
dh[t-1-i], grad['gamma'+ str(t-i)], grad['beta'+ str(t-i)] = batchnorm_backward_alt(bn[t-1-i], cache2[t-1-i])
dout[t-1-i], grad['W'+str(t-i)], grad['b'+str(t-i)] = affine_backward(dh[t-1-i], cache1[t-1-i])
else:
if self.use_dropout:
dout[t - i] = dropout_backward(dout[t - i], cache4[t - 1 - i])
dout[t - 1 - i], grads['W' + str(t - i)], grads['b' + str(t - i)] = affine_relu_backward(dout[t - i], cache3[t - 1 - i])
for i in range(self.num_layers):
grad['W'+str(i+1)] = grad['W'+str(i+1)] + self.reg * self.params['W' + str(i+1)]
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
几个ipynb：测fc，batchnorm, dropout是否正确
参考：
https://blog.csdn.net/QFire/article/details/77971749 整体结构完整
https://www.cnblogs.com/daihengchen/p/5770129.html layers.py部分代码完整