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Computes sigmoid cross entropy given logits.
tf.compat.v1.nn.sigmoid_cross_entropy_with_logits(
_sentinel=None, labels=None, logits=None, name=None
)
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 | |
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_sentinel
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Used to prevent positional parameters. Internal, do not use. |
labels
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A Tensor of the same type and shape as logits.
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logits
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A Tensor of type float32 or float64.
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name
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A name for the operation (optional). |
Returns | |
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A Tensor of the same shape as logits with the componentwise
logistic losses.
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Raises | |
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ValueError
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If logits and labels do not have the same shape.
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