SoftMarginLoss¶

SoftMarginLoss computes a smooth margin-based loss for binary classification. Instead of enforcing a hard margin, it uses a differentiable objective that encourages positive samples to receive large positive scores and negative samples to receive large negative scores.

The target tensor must contain only 1 or -1.

Signature¶

SoftMarginLoss(reduction="mean")

Parameters¶

Inputs¶

Returns¶

A scalar loss when using "mean" or "sum", or a tensor containing the per-element losses when using "none".

Formula¶

For each prediction:

Loss = log(1 + exp(-y × x))

where:

• x is the predicted score.
• y is the target label (1 or -1).

Internally, Aakaar uses a numerically stable formulation equivalent to this expression.

Example¶

import aakaar
from aakaar.losses import SoftMarginLoss

scores = aakaar.tensor([
    2.1,
    -1.5,
    0.8,
    -0.4
])

target = aakaar.tensor([
    1,
    -1,
    1,
    -1
])

criterion = SoftMarginLoss()

loss = criterion(
    scores,
    target
)

Using Different Reductions¶

Mean (default)¶

criterion = SoftMarginLoss(
    reduction="mean"
)

Returns the average loss.

Sum¶

criterion = SoftMarginLoss(
    reduction="sum"
)

Returns the sum of all losses.

None¶

criterion = SoftMarginLoss(
    reduction="none"
)

Returns the loss for each prediction individually.

Typical Training Loop¶

criterion = SoftMarginLoss()

loss = criterion(
    predictions,
    labels
)

loss.backward()
optimizer.step()

Typical Applications¶

• Binary classification
• Linear classifiers
• Margin-based learning
• Metric learning
• Representation learning
• Support vector machine-inspired models

SoftMarginLoss vs HingeEmbeddingLoss¶

Notes¶

• Expects the target tensor to contain only 1 or -1.
• Accepts raw prediction scores (logits).
• Uses a numerically stable implementation internally.
• Supports "mean", "sum", and "none" reductions.
• Suitable for binary classification tasks that benefit from a smooth margin-based objective.