log_cosh

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log_cosh#

class braintools.metric.log_cosh(predictions, targets=None, axis=None, reduction='none')#

Calculate the log-cosh loss for a set of predictions.

log(cosh(x)) is approximately (x ** 2) / 2 for small x and abs(x) - log(2) for large x. It is a twice differentiable alternative to the Huber loss.

Parameters:

  • predictions (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – A vector of arbitrary shape [...].

  • targets (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – A vector with a shape broadcastable to predictions. If not provided then it is assumed to be a vector of zeros. Inputs must be dimensionless (log(cosh(x)) is only defined for a dimensionless argument).

  • axis (int | tuple[int, ...] | None) – Axis or axes along which to reduce when reduction is 'mean' or 'sum'. If None, reduction (if any) is over all elements.

  • reduction (str) –

    Reduction operation to apply:

    • 'none': return element-wise losses with the same shape as predictions (backward-compatible default),

    • 'mean': return the mean of the losses,

    • 'sum': return the sum of the losses.

Returns:

The log-cosh loss with the same shape as predictions when reduction='none'; otherwise the reduced value.

Return type:

Array | ndarray | bool | number | bool | int | float | complex | Quantity

Notes

The loss is computed with the numerically stable, gradient-safe identity

\[\log(\cosh(x)) = |x| + \operatorname{softplus}(-2 |x|) - \log 2,\]

which avoids overflow in cosh/exp and yields finite gradients even for very large |x| (e.g. |x| = 500).

References

Examples

>>> import jax.numpy as jnp
>>> import braintools
>>> predictions = jnp.array([0.0, 1.0, -1.0])
>>> braintools.metric.log_cosh(predictions)
Array([0.       , 0.4337808, 0.4337808], dtype=float32)
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