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batch_norm2d.py
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try:
import cupy as np
is_cupy_available = True
except:
import numpy as np
is_cupy_available = False
class BatchNormalization2D():
"""
Applies batch normalization to the input data
---------------------------------------------
Args:
`momentum` (float): the momentum parameter of the moving mean
`epsilon` (float): the epsilon parameter of the algorithm
Returns:
output: the normalized input data with same shape
References:
https://kevinzakka.github.io/2016/09/14/batch_normalization/
https://agustinus.kristia.de/techblog/2016/07/04/batchnorm/
https://stackoverflow.com/questions/67968913/derivative-of-batchnorm2d-in-pytorch
"""
def __init__(self, features_num, momentum = 0.99, epsilon = 0.001, input_shape = None, data_type = np.float32):
self.features_num = features_num
self.momentum = momentum
self.epsilon = epsilon
self.gamma = None
self.beta = None
self.mean = None
self.var = None
self.moving_mean = None
self.moving_var = None
self.optimizer = None
self.input_shape = input_shape
self.data_type = data_type
self.build()
def set_optimizer(self, optimizer):
self.optimizer = optimizer
def build(self):
self.gamma = np.ones(self.features_num).astype(self.data_type)
self.beta = np.zeros(self.features_num).astype(self.data_type)
self.vg, self.mg = np.zeros_like(self.gamma).astype(self.data_type), np.zeros_like(self.gamma).astype(self.data_type)
self.vg_hat, self.mg_hat = np.zeros_like(self.gamma).astype(self.data_type), np.zeros_like(self.gamma).astype(self.data_type)
self.vb, self.mb = np.zeros_like(self.gamma).astype(self.data_type), np.zeros_like(self.gamma).astype(self.data_type)
self.vb_hat, self.mb_hat = np.zeros_like(self.gamma).astype(self.data_type), np.zeros_like(self.gamma).astype(self.data_type)
self.output_shape = self.input_shape
def forward(self, X, training = True):
self.input_data = X
self.batch_size = X.shape[0]
if self.input_shape is None:
self.input_shape = self.input_data.shape[1:]
self.build()
if self.moving_mean is None: self.moving_mean = np.mean(self.input_data, axis = (0, 2, 3))
if self.moving_var is None: self.moving_var = np.var(self.input_data, axis = (0, 2, 3))
if training == True:
self.mean = np.mean(self.input_data, axis = (0, 2, 3))
self.var = np.var(self.input_data, axis = (0, 2, 3))
self.moving_mean = self.momentum * self.moving_mean + (1.0 - self.momentum) * self.mean
self.moving_var = self.momentum * self.moving_var + (1.0 - self.momentum) * self.var
else:
self.mean = self.moving_mean
self.var = self.moving_var
self.X_centered = (self.input_data - self.mean[None, :, None, None])
self.stddev_inv = 1 / np.sqrt(self.var + self.epsilon)
X_hat = self.X_centered * self.stddev_inv[None, :, None, None]
self.output_data = self.gamma[None, :, None, None] * X_hat + self.beta[None, :, None, None]
return self.output_data
def backward(self, error):
B = self.input_data.shape[0] * self.input_data.shape[2] * self.input_data.shape[3]
X_hat = self.X_centered * self.stddev_inv[None, :, None, None]
dX_hat = error * self.gamma[None, :, None, None]
dvar = (-0.5 * dX_hat * self.X_centered).sum((0, 2, 3), keepdims=True) * (self.stddev_inv[None, :, None, None] ** 3.0)
dmu = (- self.stddev_inv[None, :, None, None] * dX_hat).sum((0, 2, 3), keepdims = True) + (dvar * (-2.0 * self.X_centered).sum((0, 2, 3), keepdims = True) / B)
output_error = (dX_hat * self.stddev_inv[None, :, None, None]) + (dvar * 2.0 * self.X_centered / B) + (dmu / B)
self.grad_gamma = (error * X_hat).sum((0, 2, 3))
self.grad_beta = (error).sum((0, 2, 3))
return output_error
def update_weights(self, layer_num):
self.gamma, self.vg, self.mg, self.vg_hat, self.mg_hat = self.optimizer.update(self.grad_gamma, self.gamma, self.vg, self.mg, self.vg_hat, self.mg_hat, layer_num)
self.beta, self.vb, self.mb, self.vb_hat, self.mb_hat = self.optimizer.update(self.grad_beta, self.beta, self.vb, self.mb, self.vb_hat, self.mb_hat, layer_num)
def get_grads(self):
return self.grad_gamma, self.grad_beta
def set_grads(self, grads):
self.grad_gamma, self.grad_beta = grads