binary_crossentropy和categorical_crossentropy是常用的用于多分类问题中的损失函数。

binary_crossentropy用于二分类问题，即每个样本只有两个可能的标签。对于每个样本，该函数计算真实标签和预测标签之间的差距。例如：

import tensorflow as tf
from tensorflow.keras.losses import binary_crossentropy

y_true = [[1], [0], [1], [0]]
y_pred = [[0.9], [0.2], [0.8], [0.1]]

loss = binary_crossentropy(y_true, y_pred)
print(loss.numpy()) # [0.10536055 0.22314353 0.22314353 0.10536055]

categorical_crossentropy则用于多分类问题，即每个样本可以拥有多个标签。对于每个样本，该函数计算真实标签和预测标签之间的交叉熵。例如：

import tensorflow as tf
from tensorflow.keras.losses import categorical_crossentropy

y_true = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
y_pred = [[0.9, 0.05, 0.05], [0.05, 0.9, 0.05], [0.05, 0.05, 0.9]]

loss = categorical_crossentropy(y_true, y_pred)
print(loss.numpy()) # [0.10536055 0.10536055 0.10536055]

需要注意的是，如果每个样本只有一个标签，则可以将categorical_crossentropy视为binary_crossentropy的特例。例如：

import tensorflow as tf
from tensorflow.keras.losses import categorical_crossentropy

y_true = [0, 1, 2]
y_pred = [[0.9, 0.05, 0.05], [0.05, 0.9, 0.05], [0.05, 0.05, 0.9]]

loss = categorical_crossentropy(tf.one_hot(y_true, depth=3), y_pred)
print(loss.numpy()) # [0.10536055 0.10536055 0.10536055]