# tf.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/v2.14.0/tensorflow/python/ops/nn_impl.py#L251-L340) |

Computes a weighted cross entropy.

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

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.

    labels = tf.constant([1., 0.5, 0.])
    logits = tf.constant([1.5, -0.1, -10.])
    tf.nn.weighted_cross_entropy_with_logits(
        labels=labels, logits=logits, pos_weight=tf.constant(1.5)).numpy()
    array([3.0211994e-01, 8.8049585e-01, 4.5776367e-05], dtype=float32)
    tf.nn.weighted_cross_entropy_with_logits(
        labels=labels, logits=logits, pos_weight=tf.constant(0.5)).numpy()
    array([1.00706644e-01, 5.08297503e-01, 4.57763672e-05], dtype=float32)

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| ## Args ||
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| `labels` | A `Tensor` of the same type and shape as `logits`, with values between 0 and 1 inclusive. |
| `logits` | A `Tensor` of type `float32` or `float64`, any real numbers. |
| `pos_weight` | A coefficient to use on the positive examples, typically a scalar but otherwise broadcastable to the shape of `logits`. Its value should be non-negative. |
| `name` | A name for the operation (optional). |

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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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