自学教程：keras中两种交叉熵损失函数的探讨

def binary_crossentropy(target, output, from_logits=False):
    """Binary crossentropy between an output tensor and a target tensor.

    # Arguments
        target: A tensor with the same shape as `output`.
        output: A tensor.
        from_logits: Whether `output` is expected to be a logits tensor.
            By default, we consider that `output`
            encodes a probability distribution.

    # Returns
        A tensor.
    """
    # Note: tf.nn.sigmoid_cross_entropy_with_logits
    # expects logits, Keras expects probabilities.
    if not from_logits:
        # transform back to logits
        _epsilon = _to_tensor(epsilon(), output.dtype.base_dtype)
        output = tf.clip_by_value(output, _epsilon, 1 - _epsilon)
        output = tf.log(output / (1 - output))

    return tf.nn.sigmoid_cross_entropy_with_logits(labels=target,
                                                   logits=output)


def categorical_crossentropy(target, output, from_logits=False, axis=-1):
    """Categorical crossentropy between an output tensor and a target tensor.

    # Arguments
        target: A tensor of the same shape as `output`.
        output: A tensor resulting from a softmax
            (unless `from_logits` is True, in which
            case `output` is expected to be the logits).
        from_logits: Boolean, whether `output` is the
            result of a softmax, or is a tensor of logits.
        axis: Int specifying the channels axis. `axis=-1`
            corresponds to data format `channels_last`,
            and `axis=1` corresponds to data format
            `channels_first`.

    # Returns
        Output tensor.

    # Raises
        ValueError: if `axis` is neither -1 nor one of
            the axes of `output`.
    """
    output_dimensions = list(range(len(output.get_shape())))
    if axis != -1 and axis not in output_dimensions:
        raise ValueError(
            '{}{}{}'.format(
                'Unexpected channels axis {}. '.format(axis),
                'Expected to be -1 or one of the axes of `output`, ',
                'which has {} dimensions.'.format(len(output.get_shape()))))
    # Note: tf.nn.softmax_cross_entropy_with_logits
    # expects logits, Keras expects probabilities.
    if not from_logits:
        # scale preds so that the class probas of each sample sum to 1
        output /= tf.reduce_sum(output, axis, True)
        # manual computation of crossentropy
        _epsilon = _to_tensor(epsilon(), output.dtype.base_dtype)
        output = tf.clip_by_value(output, _epsilon, 1. - _epsilon)
        return - tf.reduce_sum(target * tf.log(output), axis)
    else:
        return tf.nn.softmax_cross_entropy_with_logits(labels=target,
                                                       logits=output)

model.compile(optimizer=optimizers.Adam(lr=args.lr),
%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20loss=['binary_crossentropy'],
%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20metrics=["categorical_accuracy"]
%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20)

import tensorflow as tf
import numpy as np

def sigmoid(x):
    return 1.0/(1+np.exp(-x))

y = np.array([[1,0,0],[0,1,0],[0,0,1],[1,1,0],[0,1,0]])
logits = np.array([[12,3,2],[3,10,1],[1,2,5],[4,6.5,1.2],[3,6,1]])
y_pred = sigmoid(logits)

BCE1 = -y*np.log(y_pred)-(1-y)*np.log(1-y_pred)
print(BCE1)
[[6.14419348e-06 3.04858735e+00 2.12692801e+00]
 [3.04858735e+00 4.53988992e-05 1.31326169e+00]
 [1.31326169e+00 2.12692801e+00 6.71534849e-03]
 [1.81499279e-02 1.50231016e-03 1.46328247e+00]
 [3.04858735e+00 2.47568514e-03 1.31326169e+00]]

sess =tf.Session()
y = np.array(y).astype(np.float64)
BCE2 = sess.run(tf.nn.sigmoid_cross_entropy_with_logits(labels=y,logits=logits))

print(BCE2)
[[6.14419348e-06 3.04858735e+00 2.12692801e+00]
 [3.04858735e+00 4.53988992e-05 1.31326169e+00]
 [1.31326169e+00 2.12692801e+00 6.71534849e-03]
 [1.81499279e-02 1.50231016e-03 1.46328247e+00]
 [3.04858735e+00 2.47568514e-03 1.31326169e+00]]

print(y_pred)
[[0.99999386 0.95257413 0.88079708]
 [0.95257413 0.9999546  0.73105858]
 [0.73105858 0.88079708 0.99330715]
 [0.98201379 0.99849882 0.76852478]
 [0.95257413 0.99752738 0.73105858]]

def softmax(x):
    sum_raw = np.sum(np.exp(x),axis=-1)
    x1 = np.ones(np.shape(x))
    for i in range(np.shape(x)[0]):
        x1[i] = np.exp(x[i])/sum_raw[i]
    return x1

y_pred =softmax(logits)
CE1 = -np.sum(y*np.log(y_pred),-1)
print(CE1)
[1.68795487e-04 1.03475622e-03 6.58839038e-02 2.66698414e+00
 5.49852354e-02]
CE2 = sess.run(tf.nn.softmax_cross_entropy_with_logits_v2(labels=y,logits=logits))

print(CE2)
[1.68795487e-04 1.03475622e-03 6.58839038e-02 2.66698414e+00
 5.49852354e-02]

print(y_pred)
[[9.99831219e-01 1.23388975e-04 4.53922671e-05]
 [9.10938878e-04 9.98965779e-01 1.23282171e-04]
 [1.71478255e-02 4.66126226e-02 9.36239552e-01]
 [7.55098575e-02 9.19898383e-01 4.59175917e-03]
 [4.71234165e-02 9.46499123e-01 6.37746092e-03]]
final_BCE = np.mean(BCE1)

print(final_BCE)
1.2554386947664657
final_CE = np.mean(CE1)

print(final_CE)
0.5578113653559053