为什么在张量流中分类横熵的结果与定义不同？

Question

我正在测试 tf.keras.losses.CategoricalCrossentRopy 的结果，它为我提供了与定义不同的值。 我对跨熵的理解是：

def ce_loss_def(y_true, y_pred):
    return tf.reduce_sum(-tf.math.multiply(y_true, tf.math.log(y_pred)))

我有这样的价值：

pred = [0.1, 0.1, 0.1, 0.7]
target = [0, 0, 0, 1]
pred = tf.constant(pred, dtype = tf.float32)
target = tf.constant(target, dtype = tf.float32)

pred_2 = [0.1, 0.3, 0.1, 0.7]
target = [0, 0, 0, 1]
pred_2 = tf.constant(pred_2, dtype = tf.float32)
target = tf.constant(target, dtype = tf.float32)

根据定义，我认为它应该无视非目标类中的概率，例如：

ce_loss_def(y_true = target, y_pred = pred), ce_loss_def(y_true = target, y_pred = pred_2)

(<tf.Tensor: shape=(), dtype=float32, numpy=0.35667497>,
 <tf.Tensor: shape=(), dtype=float32, numpy=0.35667497>)

但是 tf.keras.losses.losses.categoricalcrossentropy 不给我相同的结果：

ce_loss_keras = tf.keras.losses.CategoricalCrossentropy()

ce_loss_keras(y_true = target, y_pred = pred), ce_loss_keras(y_true = target, y_pred = pred_2)

输出：

(<tf.Tensor: shape=(), dtype=float32, numpy=0.35667497>,
 <tf.Tensor: shape=(), dtype=float32, numpy=0.5389965>)

我缺少什么？

这是我用来获得此结果的笔记本的链接：

Answer 1

我发现问题是什么。矢量元素会以某种方式自动缩放，以总结为1，因为这些值是概率。

import tensorflow as tf

ce_loss = tf.keras.losses.CategoricalCrossentropy()

pred = [0.05, 0.2, 0.25, 0.5]
target = [0, 0, 0, 1]
pred = tf.constant(pred, dtype = tf.float32)
target = tf.constant(target, dtype = tf.float32)

pred_2 = [0.1, 0.3, 0.1, 0.5] # pred_2 has P(class2) = 0.3, instead of P(class2) = 0.1.
target = [0, 0, 0, 1]
pred_2 = tf.constant(pred_2, dtype = tf.float32)
target = tf.constant(target, dtype = tf.float32)

c1, c2 = ce_loss(y_true = target, y_pred = pred), ce_loss(y_true = target, y_pred = pred_2)
print("CE loss at dafault value: {}. CE loss with different probability of non-target classes:{}".format(c1,c2))

给出

CE loss at default value: 0.6931471824645996. 
CE loss with with different probability of non-target classes:0.6931471824645996

预期的。