| Index A I | layersSample |
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layers レイヤ Sigmoid Relu Affine SoftmaxWithLoss Dropout BatchNormalization Convolution Pooling 乗算 加算 構成・方式など タスク 導入 Sample 用語 |
sampleなどはCentOS7で実施 （$ python3 xxxx.py） layers
#!/usr/bin/env python3
# layers.py
import numpy as np
from functions import *
from util import im2col, col2im
class Sigmoid:
def __init__(self):
self.out = None
def forward(self, x):
out = sigmoid(x)
self.out = out
return out
def backward(self, dout):
dx = dout * (1.0 - self.out) * self.out
return dx
class Relu:
def __init__(self):
self.mask = None # True/FalseからなるNumPy配列
def forward(self, x):
self.mask = (x ＜= 0) # 全角あり
out = x.copy()
out[self.mask] = 0
return out
def backward(self, dout):
dout[self.mask] = 0
dx = dout
return dx
class Affine:
def __init__(self, W, b):
self.W =W
self.b = b
self.x = None
self.original_x_shape = None
# 重み・バイアスパラメータの微分
self.dW = None
self.db = None
def forward(self, x):
# テンソル対応
self.original_x_shape = x.shape
x = x.reshape(x.shape[0], -1)
self.x = x
out = np.dot(self.x, self.W) + self.b
return out
def backward(self, dout):
dx = np.dot(dout, self.W.T)
self.dW = np.dot(self.x.T, dout)
self.db = np.sum(dout, axis=0)
dx = dx.reshape(*self.original_x_shape) # 入力データの形状に戻す（テンソル対応）
return dx
class SoftmaxWithLoss:
def __init__(self):
self.loss = None # 損失
self.y = None # softmaxの出力
self.t = None # 教師データ
def forward(self, x, t):
self.t = t
self.y = softmax(x)
self.loss = cross_entropy_error(self.y, self.t)
return self.loss
def backward(self, dout=1):
batch_size = self.t.shape[0]
if self.t.size == self.y.size: # 教師データがone-hot-vectorの場合
dx = (self.y - self.t) / batch_size
else:
dx = self.y.copy()
dx[np.arange(batch_size), self.t] -= 1
dx = dx / batch_size
return dx
class Dropout:
def __init__(self, dropout_ratio=0.5):
self.dropout_ratio = dropout_ratio
self.mask = None
def forward(self, x, train_flg=True):
if train_flg:
self.mask = np.random.rand(*x.shape) > self.dropout_ratio
return x * self.mask
else:
return x * (1.0 - self.dropout_ratio)
def backward(self, dout):
return dout * self.mask
class BatchNormalization:
def __init__(self, gamma, beta, momentum=0.9, running_mean=None, running_var=None):
self.gamma = gamma
self.beta = beta
self.momentum = momentum
self.input_shape = None # Conv層の場合は4次元、全結合層の場合は2次元
# テスト時に使用する平均と分散
self.running_mean = running_mean
self.running_var = running_var
# backward時に使用する中間データ
self.batch_size = None
self.xc = None
self.std = None
self.dgamma = None
self.dbeta = None
def forward(self, x, train_flg=True):
self.input_shape = x.shape
if x.ndim != 2:
N, C, H, W = x.shape
x = x.reshape(N, -1)
out = self.__forward(x, train_flg)
return out.reshape(*self.input_shape)
def __forward(self, x, train_flg):
if self.running_mean is None:
N, D = x.shape
self.running_mean = np.zeros(D)
self.running_var = np.zeros(D)
if train_flg:
mu = x.mean(axis=0)
xc = x - mu
var = np.mean(xc**2, axis=0)
std = np.sqrt(var + 10e-7)
xn = xc / std
self.batch_size = x.shape[0]
self.xc = xc
self.xn = xn
self.std = std
self.running_mean = self.momentum * self.running_mean + (1-self.momentum) * mu
self.running_var = self.momentum * self.running_var + (1-self.momentum) * var
else:
xc = x - self.running_mean
xn = xc / ((np.sqrt(self.running_var + 10e-7)))
out = self.gamma * xn + self.beta
return out
def backward(self, dout):
if dout.ndim != 2:
N, C, H, W = dout.shape
dout = dout.reshape(N, -1)
dx = self.__backward(dout)
dx = dx.reshape(*self.input_shape)
return dx
def __backward(self, dout):
dbeta = dout.sum(axis=0)
dgamma = np.sum(self.xn * dout, axis=0)
dxn = self.gamma * dout
dxc = dxn / self.std
dstd = -np.sum((dxn * self.xc) / (self.std * self.std), axis=0)
dvar = 0.5 * dstd / self.std
dxc += (2.0 / self.batch_size) * self.xc * dvar
dmu = np.sum(dxc, axis=0)
dx = dxc - dmu / self.batch_size
self.dgamma = dgamma
self.dbeta = dbeta
return dx
class Convolution:
def __init__(self, W, b, stride=1, pad=0):
self.W = W # 引数、フィルター（重み）、4次元形状（FN,C,FH,FW）
self.b = b # 引数、バイアス
self.stride = stride # 引数、ストライド
self.pad = pad # 引数、パディング
# 中間データ（backward時に使用）
self.x = None
self.col = None
self.col_W = None
# 重み・バイアスパラメータの勾配
self.dW = None
self.db = None
def forward(self, x):
FN, C, FH, FW = self.W.shape
N, C, H, W = x.shape
out_h = 1 + int((H + 2*self.pad - FH) / self.stride)
out_w = 1 + int((W + 2*self.pad - FW) / self.stride)
col = im2col(x, FH, FW, self.stride, self.pad) # 入力データを展開
col_W = self.W.reshape(FN, -1).T # フィルター（重み）を2次元配列に展開
# reshape(FN, -1)：多次元の要素配列を整形
# 形状（10,3,5,5）が、reshape(10, -1)で、形状（10,75）に整形
out = np.dot(col, col_W) + self.b
out = out.reshape(N, out_h, out_w, -1).transpose(0, 3, 1, 2)
# transpose：多次元配列の軸の順番を入れ替える。（0,1,2,3）順を、(0,3,1,2)に入れ替える。
self.x = x
self.col = col
self.col_W = col_W
return out
def backward(self, dout):
FN, C, FH, FW = self.W.shape
dout = dout.transpose(0,2,3,1).reshape(-1, FN)
self.db = np.sum(dout, axis=0)
self.dW = np.dot(self.col.T, dout)
self.dW = self.dW.transpose(1, 0).reshape(FN, C, FH, FW)
dcol = np.dot(dout, self.col_W.T)
dx = col2im(dcol, self.x.shape, FH, FW, self.stride, self.pad)
return dx
class Pooling:
def __init__(self, pool_h, pool_w, stride=1, pad=0):
self.pool_h = pool_h
self.pool_w = pool_w
self.stride = stride
self.pad = pad
self.x = None
self.arg_max = None
def forward(self, x):
N, C, H, W = x.shape
out_h = int(1 + (H - self.pool_h) / self.stride)
out_w = int(1 + (W - self.pool_w) / self.stride)
# 展開
col = im2col(x, self.pool_h, self.pool_w, self.stride, self.pad)
col = col.reshape(-1, self.pool_h*self.pool_w)
arg_max = np.argmax(col, axis=1)
# 最大値
out = np.max(col, axis=1)
# 整形
out = out.reshape(N, out_h, out_w, C).transpose(0, 3, 1, 2)
self.x = x
self.arg_max = arg_max
return out
def backward(self, dout):
dout = dout.transpose(0, 2, 3, 1)
pool_size = self.pool_h * self.pool_w
dmax = np.zeros((dout.size, pool_size))
dmax[np.arange(self.arg_max.size), self.arg_max.flatten()] = dout.flatten()
dmax = dmax.reshape(dout.shape + (pool_size,))
dcol = dmax.reshape(dmax.shape[0] * dmax.shape[1] * dmax.shape[2], -1)
dx = col2im(dcol, self.x.shape, self.pool_h, self.pool_w, self.stride, self.pad)
return dx
class MulLayer: # 乗算レイヤ
def __init__(self):
self.x = None
self.y = None
def forward(self, x, y):
self.x = x # backward()用に保持する。
self.y = y
out = x * y
return out
def backward(self, dout): # 上流から伝わってきた微分（dout）
dx = dout * self.y # x と y がひっくり返る。
dy = dout * self.x
return dx, dy
class MulLayer: # 加算レイヤ
def __init__(self):
pass # 命令「何もしない」
def forward(self, x, y):
out = x + y
return out
def backward(self, dout):
dx = dout * 1 # 上流から伝わってきた微分（dout）をそのまま下流に流す。
dy = dout * 1
return dx, dy
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