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# tf.nn.sigmoid_cross_entropy_with_logits

Computes sigmoid cross entropy given `logits`.

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.

`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).

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

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