一、均方误差

 

 

 

 

 

 

 

 

 

import tensorflow as tf

x = tf.random.normal([2, 4])
w = tf.random.normal([4, 3])
b = tf.zeros([3])
y = tf.constant([2, 0])  #标签值

with tf.GradientTape() as tape:
    tape.watch([w, b])
    prob = tf.nn.softmax(x@w+b, axis=1)
    loss = tf.reduce_mean(tf.losses.MSE(tf.one_hot(y, depth=3), prob))

grads = tape.gradient(loss, [w, b])
print(grads[0], '\n')
print(grads[1])

二、交叉熵-Entropy

 

 

 

 

 

 

 

 

 

import tensorflow as tf

x = tf.random.normal([2, 4])  #2个4维样本
w = tf.random.normal([4, 3])
b = tf.zeros([3])
y = tf.constant([2, 0])    #2个样本的实际标签

with tf.GradientTape() as tape:
    tape.watch([w, b])
    logits = x @ w + b
    loss = tf.reduce_mean(tf.losses.categorical_crossentropy(tf.one_hot(y, depth=3), logits, from_logits = True))

grads = tape.gradient(loss, [w, b])
print("w的偏导数：\n", grads[0])
print("b的偏导数：\n", grads[1])

三、熵的概念

 

 

 

 

 

 

import tensorflow as tf
import os

os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'

a = tf.fill([4],0.25)
b = tf.math.log(a) / tf.math.log(2.)  #tensorflow中默认以e为底，变为2为底。
print(b)
print(-tf.reduce_sum(a*b).numpy())

a1 = tf.constant([0.1, 0.1, 0.1, 0.7])
b1 = tf.math.log(a1) / tf.math.log(2.)  #tensorflow中默认以e为底，变为2为底。
print(-tf.reduce_sum(a1*b1).numpy())

a2 = tf.constant([0.01, 0.01, 0.01, 0.97])
b2 = tf.math.log(a2) / tf.math.log(2.)  #tensorflow中默认以e为底，变为2为底。
print(-tf.reduce_sum(a2*b2).numpy())

 

 

 

 

 

 

import tensorflow as tf
import os

os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'

#函数大写形式
criteon = tf.losses.BinaryCrossentropy() #首先声明这样一个类，对instance做一个调用。
loss = criteon([1], [0.1])
print(loss)

#函数小写的形式。直接调用就可以了。
loss1 = tf.losses.binary_crossentropy([1],[0.1])
print(loss1)

 

 

 

 

 

 

 

 

import tensorflow as tf
import os

os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'

x = tf.random.normal([1,784])
w = tf.random.normal([784,2])
b = tf.zeros(2)
logits = x@w+b
print("前向传播结果：",logits.numpy())

prob = tf.math.softmax(logits, axis=1)
print("经过softmax数值为：",prob.numpy())

loss = tf.losses.categorical_crossentropy([0,1],logits,from_logits=True)
print("交叉熵数值为：{0}".format(loss))