SmoothL1Loss¶

SmoothL1Loss computes a regression loss that behaves like Mean Squared Error (MSE) for small prediction errors and Mean Absolute Error (L1) for large prediction errors. Compared to HuberLoss, the transition between the quadratic and linear regions is controlled by the beta parameter.

This loss is widely used in object detection, bounding box regression, and other robust regression tasks.

Signature¶

SmoothL1Loss(
    beta=1.0,
    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¶

Let

d = |pred − target|

Then the Smooth L1 loss is

           0.5 × d² / beta          if d < beta

Loss =

           d − 0.5 × beta           if d ≥ beta

Small errors are penalized quadratically, while larger errors are penalized linearly.

Example¶

import aakaar
from aakaar.losses import SmoothL1Loss

prediction = aakaar.tensor([
    2.3,
    1.7,
    4.2
])

target = aakaar.tensor([
    2.0,
    2.0,
    4.0
])

criterion = SmoothL1Loss()

loss = criterion(
    prediction,
    target
)

Using a Custom Beta¶

criterion = SmoothL1Loss(
    beta=0.5
)

Smaller values of beta make the loss behave more like L1Loss, while larger values make it closer to MSELoss.

Using Different Reductions¶

Mean (default)¶

criterion = SmoothL1Loss(
    reduction="mean"
)

Sum¶

criterion = SmoothL1Loss(
    reduction="sum"
)

None¶

criterion = SmoothL1Loss(
    reduction="none"
)

Returns the loss for every prediction individually.

Typical Training Loop¶

criterion = SmoothL1Loss()

loss = criterion(
    predictions,
    targets
)

loss.backward()
optimizer.step()

SmoothL1Loss vs HuberLoss¶

Typical Applications¶

• Bounding box regression
• Object detection
• Regression
• Pose estimation
• Time-series forecasting
• Robust machine learning

Notes¶

• Combines the advantages of MSELoss and L1Loss.
• Uses the beta parameter to determine when to switch from quadratic to linear loss.
• Supports "mean", "sum", and "none" reductions.
• Frequently used in object detection models because it is less sensitive to outliers than MSELoss.