Keras/tensorflow的sigmoid和crossentropy为什么精度低?

在计算损失函数时,由于数值的稳定性,概率值(即sigmoid函数的输出)被截断。

binary_crossentropy 因为损失会导致 中的函数 losses.py

def binary_crossentropy(y_true, y_pred):
    return K.mean(K.binary_crossentropy(y_true, y_pred), axis=-1)

如您所见,它反过来调用等效的后端函数。在使用Tensorflow作为后端的情况下,这将导致调用 二元交叉熵 tensorflow_backend.py 文件:

def binary_crossentropy(target, output, from_logits=False):
    """ Docstring ..."""

    # 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)

如你所见 from_logits 参数设置为 False 默认情况下。因此,if条件的计算结果为true,结果输出中的值被剪裁到范围 [epsilon, 1-epislon] epsilon 大于 1-epsilon . 这就解释了为什么 二元交叉熵 损失也是有界的。

common.py 文件:

_EPSILON = 1e-7

def epsilon():
    """Returns the value of the fuzz factor used in numeric expressions.
    # Returns
        A float.
    # Example
    ```python
        >>> keras.backend.epsilon()
        1e-07
    ```
    """
    return _EPSILON

如果出于任何原因,您希望获得更高的精度,也可以使用 set_epsilon

def set_epsilon(e):
    """Sets the value of the fuzz factor used in numeric expressions.
    # Arguments
        e: float. New value of epsilon.
    # Example
    ```python
        >>> from keras import backend as K
        >>> K.epsilon()
        1e-07
        >>> K.set_epsilon(1e-05)
        >>> K.epsilon()
        1e-05
    ```
    """
    global _EPSILON
    _EPSILON = e

但是,请注意,将epsilon设置为极低的正值或零,可能会破坏整个kera计算的稳定性。

我认为 keras , 让我们追踪一下 凯拉斯 计算

第一,

def binary_crossentropy(y_true, y_pred):
    return K.mean(K.binary_crossentropy(y_true, y_pred), axis=-1)

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)

通知 tf.clip_by_value 用于 数值稳定性

binary_crossentropy tf.nn.sigmoid_cross_entropy_with_logits 和自定义损失函数(删除谷限幅)

import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf
from keras.models import Sequential
from keras.layers import Dense
import keras

# keras
model = Sequential()
model.add(Dense(units=1, activation='sigmoid', input_shape=(
    1,), weights=[np.ones((1, 1)), np.zeros(1)]))
# print(model.get_weights())
model.compile(loss='binary_crossentropy',
              optimizer='adam', metrics=['accuracy'])

# tensorflow
G = tf.Graph()
with G.as_default():
    x_holder = tf.placeholder(dtype=tf.float32, shape=(2,))
    y_holder = tf.placeholder(dtype=tf.float32, shape=(2,))
    entropy = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(
        logits=x_holder, labels=y_holder))
sess = tf.Session(graph=G)


# keras with custom loss function
def customLoss(target, output):
    # 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))
    output = tf.log(output / (1 - output))
    return tf.nn.sigmoid_cross_entropy_with_logits(labels=target,
                                                   logits=output)
model_m = Sequential()
model_m.add(Dense(units=1, activation='sigmoid', input_shape=(
    1,), weights=[np.ones((1, 1)), np.zeros(1)]))
# print(model.get_weights())
model_m.compile(loss=customLoss,
                optimizer='adam', metrics=['accuracy'])


N = 100
xaxis = np.linspace(10, 20, N)
keras_ce = np.zeros(N)
tf_ce = np.zeros(N)
my_ce = np.zeros(N)
keras_custom = np.zeros(N)

y = np.array([0, 1])
for i, a in enumerate(xaxis):
    x = np.array([-a, a])
    # cross-entropy computed by keras/tensorflow
    keras_ce[i] = model.evaluate(x, y)[0]
    my_ce[i] = np.log(1+np.exp(-a))  # My own computation
    tf_ce[i] = sess.run(entropy, feed_dict={x_holder: x, y_holder: y})
    keras_custom[i] = model_m.evaluate(x, y)[0]
# print(model.get_weights())

plt.plot(xaxis, keras_ce, label='keras')
plt.plot(xaxis, my_ce, 'b',  label='my_ce')
plt.plot(xaxis, tf_ce, 'r:', linewidth=5, label='tensorflow')
plt.plot(xaxis, keras_custom, '--', label='custom loss')
plt.xlabel('a')
plt.ylabel('xentropy')
plt.yscale('log')
plt.legend()
plt.savefig('compare.jpg')
plt.show()