l2_loss

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l2_loss#

class braintools.metric.l2_loss(predictions, targets=None, axis=None, reduction='none')#

Calculate the L2 loss for a set of predictions.

The L2 loss is half the squared error:

\[\text{L2 loss} = \frac{1}{2} (y - \hat{y})^2\]
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 the same shape as predictions (shape equality is asserted; no broadcasting). If not provided then it is assumed to be a vector of zeros.

  • 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:

Element-wise squared differences scaled by 0.5 when reduction='none'; otherwise the reduced value.

Return type:

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

Notes

The 0.5 factor is standard in “Pattern Recognition and Machine Learning” by Bishop, but not in “The Elements of Statistical Learning” by Tibshirani.

For brainunit.Quantity inputs the result carries squared units (e.g. mV inputs produce a mV ** 2 result), since the error is squared element-wise.

References

Examples

>>> import jax.numpy as jnp
>>> import braintools
>>> predictions = jnp.array([1.0, 2.0, 3.0])
>>> targets = jnp.array([1.5, 2.5, 2.0])
>>> braintools.metric.l2_loss(predictions, targets)
Array([0.125, 0.125, 0.5  ], dtype=float32)
>>> braintools.metric.l2_loss(predictions, targets, reduction='mean')
Array(0.25, dtype=float32)
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