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# tf.nn.sigmoid_cross_entropy_with_logits

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

Defined in `tensorflow/python/ops/nn_impl.py`.

See the guide: Neural Network > Classification

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.

#### Args:

• `_sentinel`: Used to prevent positional parameters. Internal, do not use.
• `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.

© 2018 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/api_docs/python/tf/nn/sigmoid_cross_entropy_with_logits