BCELoss¶

BCELoss computes the Binary Cross-Entropy (BCE) loss between predicted probabilities and target labels. It is commonly used for binary classification and multi-label classification tasks where the model outputs probabilities in the range [0, 1].

Unlike BCEWithLogitsLoss, this loss expects the input to already be probabilities (typically produced by a sigmoid activation).

Signature¶

BCELoss(reduction='mean')

Parameters¶

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 = -(y · log(p) + (1 - y) · log(1 - p))

where:

• p is the predicted probability.
• y is the target value (0 or 1).

Example¶

import aakaar
from aakaar.losses import BCELoss

pred = aakaar.tensor([
    [0.95],
    [0.12],
    [0.81]
])

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

criterion = BCELoss()

loss = criterion(pred, target)

Using Different Reductions¶

Mean (default)¶

criterion = BCELoss(reduction="mean")

Returns the average loss across all elements.

Sum¶

criterion = BCELoss(reduction="sum")

Returns the sum of all element-wise losses.

None¶

criterion = BCELoss(reduction="none")

Returns the individual loss for every element.

Typical Training Loop¶

criterion = BCELoss()

predictions = model(inputs)

loss = criterion(predictions, targets)

loss.backward()
optimizer.step()

The model should output probabilities, typically by applying a sigmoid activation before computing the loss.

BCELoss vs BCEWithLogitsLoss¶

Notes¶

• Expects predicted values in the range [0, 1].
• Targets should typically contain values of 0 or 1.
• Uses a small epsilon internally to improve numerical stability when computing logarithms.
• Supports "mean", "sum", and "none" reductions.
• For models that output raw logits, prefer using BCEWithLogitsLoss instead.