单输出感知机及其梯度

目录

• recap
• Perceptron
  • Derivative

recap

• (y = XW + b)

• (y = sum{x_i}*w_i + b)

Perceptron

• (x_i^0) i表示当成第i个节点
• (w_{ij}^0) 表示当层的第i个节点，j表示下一个隐藏层的第j个节点
• (sigma) 表示激活函数后的节点
• E表示error值
• t表示target值

Derivative

• (E=frac{1}{2}(O_0^1-t)^2)

import tensorflow as tf

x = tf.random.normal([1, 3])
w = tf.ones([3, 1])
b = tf.ones([1])
y = tf.constant([1])

with tf.GradientTape() as tape:
    tape.watch([w, b])
    prob = tf.sigmoid(x @ w + b)
    loss = tf.reduce_mean(tf.losses.MSE(y, prob))

grads = tape.gradient(loss, [w, b])

[<tf.Tensor: id=203, shape=(3, 1), dtype=float32, numpy=
 array([[-0.00047306],
        [-0.00288958],
        [-0.00280226]], dtype=float32)>,
 <tf.Tensor: id=201, shape=(1,), dtype=float32, numpy=array([-0.00275796], dtype=float32)>]

grads[0]

<tf.Tensor: id=203, shape=(3, 1), dtype=float32, numpy=
array([[-0.00047306],
       [-0.00288958],
       [-0.00280226]], dtype=float32)>

grads[1]

<tf.Tensor: id=201, shape=(1,), dtype=float32, numpy=array([-0.00275796], dtype=float32)>