L1Loss¶

L1Loss computes the Mean Absolute Error (MAE) between predicted values and target values. It measures the average absolute difference between predictions and ground-truth values, making it less sensitive to outliers than MSELoss.

Because the error grows linearly, large prediction errors do not dominate the loss as strongly as they do with squared-error losses.

Signature¶

L1Loss(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 = |pred − target|

The final loss is obtained according to the selected reduction method.

Example¶

import aakaar
from aakaar.losses import L1Loss

prediction = aakaar.tensor([
    2.5,
    1.8,
    4.1
])

target = aakaar.tensor([
    2.0,
    2.0,
    3.8
])

criterion = L1Loss()

loss = criterion(
    prediction,
    target
)

Using Different Reductions¶

Mean (default)¶

criterion = L1Loss(
    reduction="mean"
)

Returns the average absolute error.

Sum¶

criterion = L1Loss(
    reduction="sum"
)

Returns the sum of all absolute errors.

None¶

criterion = L1Loss(
    reduction="none"
)

Returns the absolute error for every element individually.

Typical Training Loop¶

criterion = L1Loss()

predictions = model(inputs)

loss = criterion(
    predictions,
    targets
)

loss.backward()
optimizer.step()

L1Loss vs MSELoss¶

Typical Applications¶

• Regression
• Time-series forecasting
• Image restoration
• Signal processing
• Robust machine learning models

Notes¶

• Computes the absolute difference between predictions and targets.
• Less sensitive to outliers than MSELoss.
• Supports "mean", "sum", and "none" reductions.
• Suitable for regression tasks where robustness to occasional large errors is desired.
• Uses the tensor abs() operation internally.