多输出感知机及其梯度

目录

• Multi-output Perceptron

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Multi-output Perceptron

\[E=\frac{1}{2}\sum(O_i^1-t_i)^2 \]

对于多输出感知机，每个输出元只和输出元上的x和w和\(\sigma\)有关。

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])

with tf.GradientTape() as tape:
    tape.watch([w, b])
    # axis=1，表示结果[b,3]中的3这个维度为概率
    prob = tf.nn.softmax(x @ w + b, axis=1)
    # 2 --> 001; 0 --> 100
    loss = tf.reduce_mean(tf.losses.MSE(tf.one_hot(y, depth=3), prob))

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

grads[0]

<tf.Tensor: id=92, shape=(4, 3), dtype=float32, numpy=
array([[ 0.00842961, -0.02221732,  0.01378771],
       [ 0.02969089, -0.04625662,  0.01656573],
       [ 0.05807886, -0.08139262,  0.02331377],
       [-0.06571108,  0.11157083, -0.04585974]], dtype=float32)>

grads[1]

<tf.Tensor: id=90, shape=(3,), dtype=float32, numpy=array([-0.05913186,  0.09886257, -0.03973071], dtype=float32)>