# tf.compat.v1.nn.weighted_cross_entropy_with_logits

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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.13.1/tensorflow/python/ops/nn_impl.py#L343-L405) |

Computes a weighted cross entropy. (deprecated arguments)

    tf.compat.v1.nn.weighted_cross_entropy_with_logits(
        labels=None, logits=None, pos_weight=None, name=None, targets=None
    )

> [!WARNING]
> **Deprecated:** SOME ARGUMENTS ARE DEPRECATED: `(targets)`. They will be removed in a future version. Instructions for updating: targets is deprecated, use labels instead

This is like `sigmoid_cross_entropy_with_logits()` except that `pos_weight`,
allows one to trade off recall and precision by up- or down-weighting the
cost of a positive error relative to a negative error.

The usual cross-entropy cost is defined as:

    labels * -log(sigmoid(logits)) +
        (1 - labels) * -log(1 - sigmoid(logits))

A value `pos_weight > 1` decreases the false negative count, hence increasing
the recall.
Conversely setting `pos_weight < 1` decreases the false positive count and
increases the precision.
This can be seen from the fact that `pos_weight` is introduced as a
multiplicative coefficient for the positive labels term
in the loss expression:

    labels * -log(sigmoid(logits)) * pos_weight +
        (1 - labels) * -log(1 - sigmoid(logits))

For brevity, let `x = logits`, `z = labels`, `q = pos_weight`.
The loss is:

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

Setting `l = (1 + (q - 1) * z)`, to ensure stability and avoid overflow,
the implementation uses

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

`logits` and `labels` must have the same type and shape.

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| ## Args ||
|---|---|
| `labels` | A `Tensor` of the same type and shape as `logits`. |
| `logits` | A `Tensor` of type `float32` or `float64`. |
| `pos_weight` | A coefficient to use on the positive examples. |
| `name` | A name for the operation (optional). |
| `targets` | Deprecated alias for labels. |

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| ## Returns ||
|---|---|
| A `Tensor` of the same shape as `logits` with the componentwise weighted logistic losses. ||

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| ## Raises ||
|---|---|
| `ValueError` | If `logits` and `labels` do not have the same shape. |

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