multi_margin_loss

→Tensor

multi_margin_loss(x: Tensor, target: Tensor, p: int = 1, margin: float = 1.0, weight: Tensor | None = None, reduction: str = 'mean')

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Multi-class hinge (margin) loss — Crammer-Singer SVM objective.

A non-probabilistic alternative to cross_entropy for multi-class classification: instead of fitting a softmax distribution, it requires the true-class score to exceed every other class score by at least margin. Frequently used in structured prediction and as a drop-in for hinge-style losses in metric learning.

Parameters

xTensor

Class scores of shape

(N, C)

targetTensor

Integer class indices of shape

(N,)

pint= 1

Power applied to each hinge term — 1 for the standard hinge loss, 2 for the smoother squared-hinge variant (default 1).

marginfloat= 1.0

Required minimum score gap between the true class and every competitor (default 1.0).

weightTensor or None= None

Per-class weight vector of shape

(C,)

. Each sample contribution is scaled by the weight of its true class.

reductionstr= 'mean'

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

Returns

Tensor

Scalar or per-sample tensor of shape $(N,)$ .

Notes

Per-sample loss:

L_i = \frac{1}{C} \sum_{j \ne t_i} \max\!\big(0,\; \text{margin} - x_{i, t_i} + x_{i, j}\big)^p

Samples whose true-class score already dominates all competitors by margin produce zero loss and zero gradient — like the binary SVM hinge, only the support vectors contribute to the update.

Examples

>>> import lucid
>>> from lucid.nn.functional import multi_margin_loss
>>> scores = lucid.tensor([[2.0, 0.5, 0.1]])
>>> target = lucid.tensor([0], dtype=lucid.int32)
>>> multi_margin_loss(scores, target)
Tensor(0.0)