MSELoss¶

MSELoss computes the Mean Squared Error (MSE) between predicted values and target values. It is one of the most widely used loss functions for regression tasks, penalizing larger prediction errors more heavily than smaller ones.

Because the error is squared, large mistakes contribute significantly more to the final loss.

Signature¶

MSELoss(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)²

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

Example¶

import aakaar
from aakaar.losses import MSELoss

prediction = aakaar.tensor([
    2.4,
    1.7,
    3.9
])

target = aakaar.tensor([
    2.0,
    2.1,
    4.2
])

criterion = MSELoss()

loss = criterion(
    prediction,
    target
)

Using Different Reductions¶

Mean (default)¶

criterion = MSELoss(
    reduction="mean"
)

Returns the average squared error.

Sum¶

criterion = MSELoss(
    reduction="sum"
)

Returns the sum of all squared errors.

None¶

criterion = MSELoss(
    reduction="none"
)

Returns the squared error for every element individually.

Typical Training Loop¶

criterion = MSELoss()

predictions = model(inputs)

loss = criterion(
    predictions,
    targets
)

loss.backward()
optimizer.step()

MSELoss vs L1Loss¶

Typical Applications¶

• Linear regression
• Neural network regression
• Time-series forecasting
• Function approximation
• Image reconstruction
• Scientific computing

Notes¶

• Computes the squared difference between predictions and targets.
• Large prediction errors contribute disproportionately to the final loss.
• Supports "mean", "sum", and "none" reductions.
• Commonly used as the default loss for regression problems.
• Suitable when large prediction errors should be penalized more heavily than small ones.