單輸出感知機及其梯度

目錄

• recap
• Perceptron
  • Derivative

recap

• \(y = XW + b\)

• \(y = \sum{x_i}*w_i + b\)

Perceptron

• \(x_i^0\) i表示當成第i個節點
• \(w_{ij}^0\) 表示當層的第i個節點，j表示下一個隱藏層的第j個節點
• \(\sigma\) 表示激活函數後的節點
• 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)>