soft_margin_loss

→Tensor

soft_margin_loss(input: Tensor, target: Tensor, reduction: str = 'mean')

source

Logistic (softplus) loss for binary classification with ±1 labels.

A "soft" variant of the binary hinge loss: instead of the piecewise-linear $\max(0, 1 - y\,x)$ , it uses the smooth surrogate $\log(1 + e^{-y\,x})$ — which is the negative-log-likelihood of a logistic model with labels in $\{-1, +1\}$ . Equivalent to binary_cross_entropy_with_logits with the {0, 1} labels re-coded as $\{-1, +1\}$ .

The implementation evaluates $\mathrm{softplus}(-y\,x)$ , which is numerically stable for large |x| (no overflow, no log of near-zero values).

Parameters

inputTensor

Raw scores (logits), any shape.

targetTensor

Target tensor of the same shape, conventionally holding

\pm 1

(any real values are accepted).

reductionstr= 'mean'

"mean" (default), "sum", or "none".

Returns

Tensor

Scalar or full-shape per reduction.

Notes

Per-element loss:

L_i = \log\!\big(1 + \exp(-y_i\,x_i)\big).

Unlike the (non-smooth) hinge, every sample contributes a non-zero gradient — even correctly classified ones — but the contribution decays exponentially as $y\,x$ grows. This softness improves optimisation behaviour with first-order methods at the cost of a slightly less sparse solution.

Examples

>>> import lucid
>>> from lucid.nn.functional import soft_margin_loss
>>> x = lucid.tensor([2.0, -1.0])
>>> y = lucid.tensor([1.0, -1.0])
>>> soft_margin_loss(x, y)
Tensor(0.2284...)