recap

$y = X W + b$
$y = \sum x_{i} * w_{i} + b$

Perceptron

22-单输出感知机及其梯度-感知机模型.jpg

$x_{i}^{0}$ i表示当成第i个节点
$w_{i j}^{0}$ 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
$σ$ 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)>