MultiLabelSoftMarginLoss¶

MultiLabelSoftMarginLoss computes the binary cross-entropy loss with logits for multi-label classification tasks. Unlike multi-class classification, where each sample belongs to exactly one class, multi-label classification allows each sample to belong to multiple classes simultaneously.

Internally, this loss computes BCEWithLogitsLoss for each class and then averages the loss across all classes for every sample.

Signature¶

MultiLabelSoftMarginLoss(reduction="mean")

Parameters¶

Parameter	Type	Description
`reduction`	`str`	Specifies the reduction to apply: `"mean"`, `"sum"`, or `"none"`. Default is `"mean"`.

Inputs¶

Input	Description
`logits`	Raw prediction scores (logits) for each class.
`target`	Target tensor containing binary labels (`0` or `1`) for each class.

Returns¶

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

Formula¶

For each class, the loss is computed using binary cross-entropy with logits:

BCE = max(x, 0) - x · y + log(1 + exp(-|x|))

where:

x is the predicted logit.
y is the target label (0 or 1).

The final loss for each sample is the average BCE across all classes.

Example¶

import aakaar
from aakaar.losses import MultiLabelSoftMarginLoss

logits = aakaar.tensor([
    [2.5, -1.3, 0.8],
    [-0.6, 1.9, 2.4]
])

targets = aakaar.tensor([
    [1, 0, 1],
    [0, 1, 1]
])

criterion = MultiLabelSoftMarginLoss()

loss = criterion(
    logits,
    targets
)

Using Different Reductions¶

Mean (default)¶

criterion = MultiLabelSoftMarginLoss(
    reduction="mean"
)

Returns the average loss across the batch.

Sum¶

criterion = MultiLabelSoftMarginLoss(
    reduction="sum"
)

Returns the sum of all sample losses.

None¶

criterion = MultiLabelSoftMarginLoss(
    reduction="none"
)

Returns the average loss for each sample individually.

Typical Training Loop¶

criterion = MultiLabelSoftMarginLoss()

logits = model(inputs)

loss = criterion(
    logits,
    targets
)

loss.backward()
optimizer.step()

Typical Applications¶

Multi-label image classification
Image tagging
Text classification with multiple labels
Medical diagnosis
Recommendation systems
Audio event detection

MultiLabelSoftMarginLoss vs BCEWithLogitsLoss¶

MultiLabelSoftMarginLoss	BCEWithLogitsLoss
Designed for multi-label classification	General binary classification loss
Computes BCE for every class	Computes BCE element-wise
Averages the loss across classes	Returns element-wise loss before reduction
Uses raw logits	Uses raw logits

Notes¶

Expects raw logits, not probabilities.
Target values should typically be 0 or 1 for each class.
Internally uses BCEWithLogitsLoss with reduction="none" before averaging across classes.
Supports "mean", "sum", and "none" reductions.
Suitable when each sample may belong to multiple classes simultaneously.