BCEWithLogitsLoss¶

BCEWithLogitsLoss computes the Binary Cross-Entropy (BCE) loss directly from raw logits. It combines a sigmoid activation and binary cross-entropy into a single numerically stable operation, making it the recommended loss for binary and multi-label classification tasks.

Unlike BCELoss, this loss does not require applying a sigmoid activation before computing the loss.

Signature¶

BCEWithLogitsLoss(reduction='mean')

Parameters¶

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

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

where:

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

This numerically stable formulation avoids overflow and underflow that can occur when applying a sigmoid separately.

Example¶

import aakaar
from aakaar.losses import BCEWithLogitsLoss

logits = aakaar.tensor([
    [2.8],
    [-1.4],
    [0.9]
])

target = aakaar.tensor([
    [1.0],
    [0.0],
    [1.0]
])

criterion = BCEWithLogitsLoss()

loss = criterion(logits, target)

Using Different Reductions¶

Mean (default)¶

criterion = BCEWithLogitsLoss(
    reduction="mean"
)

Returns the average loss across all elements.

Sum¶

criterion = BCEWithLogitsLoss(
    reduction="sum"
)

Returns the sum of all element-wise losses.

None¶

criterion = BCEWithLogitsLoss(
    reduction="none"
)

Returns the individual loss for every prediction.

Typical Training Loop¶

criterion = BCEWithLogitsLoss()

logits = model(inputs)

loss = criterion(logits, targets)

loss.backward()
optimizer.step()

Notice that no sigmoid activation is applied before computing the loss.

BCEWithLogitsLoss vs BCELoss¶

BCEWithLogitsLoss	BCELoss
Expects raw logits	Expects probabilities
Applies sigmoid internally	Requires sigmoid before the loss
Numerically stable	Less numerically stable
Recommended for most training tasks	Useful when probabilities are already available

Typical Applications¶

Binary classification
Multi-label image classification
Medical image classification
Recommendation systems
Any task where each output is an independent binary prediction

Notes¶

Expects raw logits, not probabilities.
Targets should typically contain values of 0 or 1.
Uses a numerically stable formulation that combines sigmoid and binary cross-entropy into a single computation.
Supports "mean", "sum", and "none" reductions.
Recommended over BCELoss for most training pipelines due to improved numerical stability.