NLLLoss¶

NLLLoss computes the Negative Log-Likelihood (NLL) loss for classification tasks. It expects the input to contain log-probabilities rather than raw logits.

In Aakaar, this loss expects one-hot encoded targets instead of integer class indices. It is commonly used together with log_softmax or as the backend for CrossEntropyLoss.

Signature¶

NLLLoss(reduction="mean")

Parameters¶

Inputs¶

Returns¶

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

Formula¶

For each sample:

Loss = -Σ(target × log_probs)

Since the target is one-hot encoded, this effectively selects the log-probability of the correct class and negates it.

Example¶

import aakaar
from aakaar import log_softmax
from aakaar.losses import NLLLoss

logits = aakaar.tensor([
    [2.3, 0.5, -1.1],
    [0.2, 1.9, 0.8]
])

log_probs = log_softmax(
    logits,
    dim=-1
)

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

criterion = NLLLoss()

loss = criterion(
    log_probs,
    targets
)

Using Different Reductions¶

Mean (default)¶

criterion = NLLLoss(
    reduction="mean"
)

Returns the average loss across the batch.

Sum¶

criterion = NLLLoss(
    reduction="sum"
)

Returns the sum of all sample losses.

None¶

criterion = NLLLoss(
    reduction="none"
)

Returns the loss for each sample individually.

Typical Training Loop¶

criterion = NLLLoss()

log_probs = aakaar.log_softmax(
    logits,
    dim=-1
)

loss = criterion(
    log_probs,
    targets
)

loss.backward()
optimizer.step()

NLLLoss vs CrossEntropyLoss¶

Notes¶

• Expects log-probabilities, not raw logits.
• Targets must be one-hot encoded in the current version of Aakaar.
• Commonly used after log_softmax.
• Supports "mean", "sum", and "none" reductions.
• Serves as the underlying implementation used by CrossEntropyLoss when the fused path is not applicable.