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tf.nn.sigmoid_cross_entropy_with_logits

TensorFlow 1 version View source on GitHub

Computes sigmoid cross entropy given logits.

Aliases:

tf.nn.sigmoid_cross_entropy_with_logits(
    labels=None,
    logits=None,
    name=None
)

Used in the tutorials:

Measures the probability error in discrete classification tasks in which each class is independent and not mutually exclusive. For instance, one could perform multilabel classification where a picture can contain both an elephant and a dog at the same time.

For brevity, let x = logits, z = labels. The logistic loss is

  z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= z * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + log(1 + exp(-x))
= x - x * z + log(1 + exp(-x))

For x < 0, to avoid overflow in exp(-x), we reformulate the above

  x - x * z + log(1 + exp(-x))
= log(exp(x)) - x * z + log(1 + exp(-x))
= - x * z + log(1 + exp(x))

Hence, to ensure stability and avoid overflow, the implementation uses this equivalent formulation

max(x, 0) - x * z + log(1 + exp(-abs(x)))

logits and labels must have the same type and shape.

Args:

  • labels: A Tensor of the same type and shape as logits.
  • logits: A Tensor of type float32 or float64.
  • name: A name for the operation (optional).

Returns:

A Tensor of the same shape as logits with the componentwise logistic losses.

Raises:

  • ValueError: If logits and labels do not have the same shape.