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import sys, os
sys.path.append(os.path.realpath(os.path.dirname(os.path.realpath(__file__))))
import numpy as np
from layers import *
from dropout_layers import *
def batchnorm_forward(x, gamma, beta, bn_param):
"""
使用类似动量衰减的运行时平均，计算总体均值与方差 例如:
running_mean = momentum * running_mean + (1 - momentum) * sample_mean
running_var = momentum * running_var + (1 - momentum) * sample_var
Input:
- x: 数据(N, D)
- gamma: 缩放参数 (D,)
- beta: 平移参数 (D,)
- bn_param: 字典型，使用下列键值:
- mode: 'train' 或'test';
- eps: 保证数值稳定
- momentum: 运行时平均衰减因子
- running_mean: 形状为(D,)的运行时均值
- running_var : 形状为 (D,)的运行时方差
Returns 元组:
- out: 输出(N, D)
- cache: 用于反向传播的缓存
"""
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':
mu = 1/float(N)*np.sum(x, axis=0)
xmu = x-mu
carre = xmu**2
var = 1/float(N)*np.sum(carre, axis=0)
sqrtvar = np.sqrt(var+eps)
invvar = 1./sqrtvar
va2 = xmu*invvar
va3 = gamma*va2
out = va3+beta
running_mean = momentum*running_mean+(1.0-momentum)*mu
running_var = momentum * running_var+(1.0-momentum)*var
cache=(mu, xmu, carre, var, sqrtvar, invvar, va2, va3, gamma, beta, x, bn_param)
elif mode == 'test':
mu = running_mean
var = running_var
xhat = (x-mu)/np.sqrt(var+eps)
out = gamma*xhat+beta
cache = (mu, var, gamma, beta, bn_param)
else:
raise ValueError('无法识别的BN模式： "%s"' % mode)
bn_param['running_mean'] = running_mean
bn_param['running_var'] = running_var
return out, cache
def batchnorm_backward(dout, cache):
"""
BN反向传播
Inputs:
- dout: 上层梯度 (N, D)
- cache: 前向传播时的缓存.
Returns 元组:
- dx: 数据梯度 (N, D)
- dgamma: gamma梯度 (D,)
- dbeta: beta梯度 (D,)
"""
dx, dgamma, dbeta = None, None, None
mu, xmu, carre, var, sqrtvar, invvar, va2, va3, gamma, beta, x, bn_param=cache
eps = bn_param.get('eps', 1e-5)
N, D = dout.shape
dva3 = dout
dbeta = np.sum(dout, axis=0)
dva2 = gamma*dva3
dgamma = np.sum(va2*dva3, axis=0)
dxmu = invvar*dva2
dinvvar = np.sum(xmu*dva2, axis=0)
dsqrtvar = -1./(sqrtvar**2)*dinvvar
dvar = 0.5*(var+eps)**(-0.5)*dsqrtvar
dcarre = 1/float(N)*np.ones((carre.shape))*dvar
dxmu += 2*xmu*dcarre
dx = dxmu
dmu = -np.sum(dxmu, axis=0)
dx += 1/float(N)*np.ones((dxmu.shape))*dmu
return dx, dgamma, dbeta
def batchnorm_backward_alt(dout, cache):
"""
可选的BN反向传播
"""
dx, dgamma, dbeta = None, None, None
mu, xmu, carre, var, sqrtvar, invvar, va2, va3, gamma, beta, x, bn_param = cache
eps = bn_param.get('eps', 1e-5)
N, D = dout.shape
dbeta = np.sum(dout, axis=0)
dgamma = np.sum((x - mu) * (var + eps)**(-1. / 2.) * dout, axis=0)
dx = (1./N) * gamma * (var + eps)**(-1./2.)*(N*dout-np.sum(
dout, axis=0)-(x-mu)*(var+eps)**(-1.0)*np.sum(dout*(x-mu),axis=0))
return dx, dgamma, dbeta
def affine_bn_relu_forward(x,w,b,gamma, beta,bn_param):
x_affine,cache_affine= affine_forward(x,w,b)
x_bn,cache_bn = batchnorm_forward(x_affine,gamma, beta,bn_param)
out,cache_relu = relu_forward(x_bn)
cache = (cache_affine,cache_bn,cache_relu)
return out,cache
def affine_bn_relu_backward(dout,cache):
cache_affine,cache_bn,cache_relu = cache
drelu = relu_backward(dout,cache_relu)
dbn,dgamma, dbeta= batchnorm_backward_alt(drelu,cache_bn)
dx,dw,db = affine_backward(dbn,cache_affine)
return dx,dw,db,dgamma,dbeta
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