如果有错误，欢迎指出，不胜感激。
import numpy as np
def affine_forward(x, w, b): 第一个最简单的 affine_forward简单的前向传递，返回 out,cache
"""
Computes the forward pass for an affine (fully-connected) layer.
The input x has shape (N, d_1, ..., d_k) and contains a minibatch of N
examples, where each example x[i] has shape (d_1, ..., d_k). We will
reshape each input into a vector of dimension D = d_1 * ... * d_k, and
then transform it to an output vector of dimension M.
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
tx=x.reshape((x.shape[0],-1))
out=tx.dot(w)+b.T
cache = (x, w, b)
return out, cache
def affine_backward(dout, cache): 后向传递，ＢＰ的时候梯度向前传递的实现可以想想。 dx的计算,db的计算由于前向传递的时候出现过broadcast,所以后向传递时就是求和
"""
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
dx=dout.dot(w.T)
dx=dx.reshape(x.shape)
dw=x.reshape(x.shape[0],-1).T.dot(dout)
db=np.sum(dout,axis=0) #
# print "db is"+str(db.shape)
return dx, dw, db
def relu_forward(x): relu激励函数，后向传递的时候要截住一部分梯度
"""
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(0,x)
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): BN层，有了BN层就不太容易出现vanish gradient
"""
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 后两个是在动态更新的，因为py传list是传引用
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) dict的 get 方法
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
sample_mean=np.mean(x,axis=0)
sample_var=np.var(x,axis=0)
if mode == ‘train‘:
running_mean = momentum * running_mean + (1 - momentum) * sample_mean
running_var = momentum * running_var + (1 - momentum) * sample_var
std=np.sqrt(sample_var+eps)
out1=(x-sample_mean)/(std)
std=np.sqrt(sample_var+eps)
out2=(out1+beta)*gamma
out=out2
cache=(x,sample_mean,sample_var,std,out1,beta,gamma,eps)
elif mode == ‘test‘:
x=(x-running_mean)/np.sqrt(running_var+eps)
out1=(x+beta)*gamma
out=out1
#cache=(x,sample_mean,sample_var,std,out1,beta,gamma,eps)
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): 这个很经典 可以试着画出图表来计算 曾经因为卡eps卡了一段时间
"""
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
x,sample_mean,sample_var,std,out1,beta,gamma,eps=cache
x_n=x.shape[0]
dgamma=np.sum((out1+beta)*dout,axis=0)
dbeta=np.sum(gamma*dout,axis=0)
‘‘‘
tdout_media = dout * gamma
tdgamma = np.sum(dout * (out1 + beta),axis = 0)
tdbeta = np.sum(dout * gamma,axis = 0)
tdx = tdout_media / np.sqrt(sample_var + eps)
tdmean = -np.sum(tdout_media / np.sqrt(sample_var+eps),axis = 0)
tdstd = np.sum(-tdout_media * (x - sample_mean) / (sample_var + eps),axis = 0)
tdvar = 1./2./np.sqrt(sample_var+eps) * tdstd
tdx_minus_mean_square = tdvar / x.shape[0]
tdx_minus_mean = 2 * (x-sample_mean) * tdx_minus_mean_square
print tdx_minus_mean
tdx += tdx_minus_mean
tdmean += np.sum(-tdx_minus_mean,axis = 0)
tdx += tdmean / x.shape[0]
‘‘‘
dout1=gamma*dout
dx_minus_xmean=dout1/np.sqrt(sample_var+eps)
dx1=dx_minus_xmean
dxmean=np.sum(-dx_minus_xmean,axis=0)
dx2=np.ones((x_n,1)).dot((dxmean/x_n).reshape(1,-1))
dsqrtvar=np.sum( ((sample_mean-x)/(sample_var+eps))*dout1 ,axis=0 )
dvar=1./(2.*(np.sqrt(sample_var+eps))) *dsqrtvar
#stupid
dx3=2*(x-sample_mean)*dvar/x_n
dtest=np.sum(-dx3,axis=0)
dx=dx1+dx2+dx3
return dx, dgamma, dbeta
def batchnorm_backward_alt(dout, cache): 耐心推一下还是可以推出来的，利用示性函数和中间变量
"""
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,sample_mean,sample_var,std,out1,beta,gamma,eps=cache
n_x=x.shape[0]
dgamma=np.sum((out1+beta)*dout,axis=0)
dbeta=np.sum(gamma*dout,axis=0)
#dx=(((1-1./n_x)*gamma*(sample_var+eps)-((x-sample_mean)**2)/n_x )/((sample_var+eps)**1.5)) *dout1
dx = (1. / n_x) * gamma * (sample_var + eps)**(-1. / 2.) * (n_x * dout - np.sum(dout, axis=0)
- (x - sample_mean) * (sample_var + eps)**(-1.0) * np.sum(dout * (x - sample_mean), axis=0))
return dx, dgamma, dbeta
def dropout_forward(x, dropout_param): 也是防止过拟合
"""
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(1,x.shape[1])
mask=(mask>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): 四重循环，这个单元没让写快速的版本（估计也不太会写/：（
"""
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)
"""
N,C,H,W=x.shape
F,C,HH,WW=w.shape
pad=conv_param[‘pad‘]
stride=conv_param[‘stride‘]
H2=1+(H+2*pad-HH)/stride
W2=1+(W+2*pad-WW)/stride
out = None
out=np.zeros((N,F,H2,W2))
x_pad=np.pad(x,((0,0),(0,0),(pad,pad),(pad,pad)),mode=‘constant‘,constant_values=0)
for i in xrange(N):
for j in xrange(F):
for k in xrange(H2):
for q in xrange(W2):
out[i,j,k,q]=np.sum(w[j]*x_pad[i,:,k*stride:(k)*stride+HH,q*stride:(q)*stride+WW])+b[j]
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 wikth respect to w
- db: Gradient with respect to b
"""
dx, dw, db = None, None, None
x,w,b,conv_param=cache
pad=conv_param[‘pad‘]
stride=conv_param[‘stride‘]
N,C,H,W=x.shape
N,C,H2,W2=dout.shape
F,C,HH,WW=w.shape
F=b.shape[0]
x_pad=np.pad(x,((0,0),(0,0),(pad,pad),(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.zeros_like(b)
for i in xrange(N):
for j in xrange(H2):
for k in xrange(W2):
for q in xrange(F):
dw[q]+=dout[i][q][j][k]*x_pad[i,:,j*stride:j*stride+HH,k*stride:k*stride+WW]
db[q]+=dout[i][q][j][k]
dx_pad[i,:,j*stride:j*stride+HH,k*stride:k*stride+WW]+=dout[i][q][j][k]*w[q]
dx=dx_pad[:,:,pad:H+pad,pad:W+pad]
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
stride=pool_param[‘stride‘]
pool_height=pool_param[‘pool_height‘]
pool_width=pool_param[‘pool_width‘]
N,C,H,W=x.shape
H2=(H-pool_height)/stride + 1
W2=(W-pool_width)/stride + 1
out=np.zeros((N,C,H2,W2))
for n in xrange(N):
for c in xrange(C):
for h in xrange(H2):
for w in xrange(W2):
out[n,c,h,w]=np.max(x[n,c,h*stride:h*stride+pool_width,w*stride:w*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
stride=pool_param[‘stride‘]
pool_height=pool_param[‘pool_height‘]
pool_width=pool_param[‘pool_width‘]
N,C,H,W=x.shape
N,C,H2,W2=dout.shape
dx=np.zeros_like(x)
for n in xrange(N):
for c in xrange(C):
for h in xrange(H2):
for w in xrange(W2):
window=x[n,c,h*stride:h*stride+pool_height,w*stride:w*stride+pool_width]
t=np.max(window)
#pass by yinyong ----sf
dx[n,c,h*stride:h*stride+pool_height,w*stride:w*stride+pool_width] = (window==t)*dout[n][c][h][w]
return dx
def spatial_batchnorm_forward(x, gamma, beta, bn_param): 套用以前的代码，让生活变的简单
"""
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=x.transpose(0,2,3,1).reshape(N*W*H,C)
out,cache=batchnorm_forward(x,gamma,beta,bn_param)
out=out.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=dout.transpose(0,2,3,1).reshape(N*H*W,C)
dx,dgamma,dbeta=batchnorm_backward(dout,cache)
dx=dx.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
n
时间： 2024-10-24 20:02:31