MarginRankingLoss¶

MarginRankingLoss measures whether one input should be ranked higher than another by at least a specified margin. It is commonly used in ranking problems, recommendation systems, learning to rank, and metric learning.

The target tensor specifies which input should receive the higher score.

Signature¶

MarginRankingLoss(
    margin=0.0,
    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¶

For each pair:

Loss = max(0, -y × (x1 - x2) + margin)

where:

• y = 1 means x1 should be greater than x2.
• y = -1 means x2 should be greater than x1.

If the desired ranking already satisfies the specified margin, the loss is zero.

Example¶

import aakaar
from aakaar.losses import MarginRankingLoss

x1 = aakaar.tensor([
    2.3,
    0.8,
    3.4
])

x2 = aakaar.tensor([
    1.5,
    1.2,
    2.8
])

target = aakaar.tensor([
    1,
    -1,
    1
])

criterion = MarginRankingLoss(
    margin=0.5
)

loss = criterion(
    x1,
    x2,
    target
)

Using a Custom Margin¶

criterion = MarginRankingLoss(
    margin=1.0
)

Larger margins require a greater separation between the two inputs before the loss becomes zero.

Using Different Reductions¶

Mean (default)¶

criterion = MarginRankingLoss(
    reduction="mean"
)

Sum¶

criterion = MarginRankingLoss(
    reduction="sum"
)

None¶

criterion = MarginRankingLoss(
    reduction="none"
)

Returns the loss for each input pair individually.

Typical Training Loop¶

criterion = MarginRankingLoss(
    margin=0.5
)

loss = criterion(
    scores_a,
    scores_b,
    labels
)

loss.backward()
optimizer.step()

Typical Applications¶

• Learning to rank
• Recommendation systems
• Information retrieval
• Metric learning
• Preference learning
• Pairwise ranking models

Notes¶

• Expects the target tensor to contain only 1 or -1.
• A target of 1 indicates that x1 should rank higher than x2.
• A target of -1 indicates that x2 should rank higher than x1.
• Supports "mean", "sum", and "none" reductions.
• Returns zero loss when the desired ranking satisfies the specified margin.
• Commonly used for pairwise ranking and preference-learning tasks.