HingeEmbeddingLoss¶

HingeEmbeddingLoss measures the similarity between input values based on binary labels. It is commonly used in metric learning, embedding learning, and Siamese neural networks, where the objective is to make similar samples close together while keeping dissimilar samples sufficiently far apart.

The target tensor must contain only 1 or -1.

Signature¶

HingeEmbeddingLoss(
    margin=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¶

For each element:

if y = 1:
    Loss = x

if y = -1:
    Loss = max(0, margin - x)

Positive pairs are encouraged to have small distances, while negative pairs are penalized only when their distance is less than the specified margin.

Example¶

import aakaar
from aakaar.losses import HingeEmbeddingLoss

distance = aakaar.tensor([
    0.2,
    1.5,
    0.8,
    2.3
])

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

criterion = HingeEmbeddingLoss()

loss = criterion(
    distance,
    target
)

Using a Custom Margin¶

criterion = HingeEmbeddingLoss(
    margin=2.0
)

Increasing the margin requires negative pairs to be farther apart before their loss becomes zero.

Using Different Reductions¶

Mean (default)¶

criterion = HingeEmbeddingLoss(
    reduction="mean"
)

Sum¶

criterion = HingeEmbeddingLoss(
    reduction="sum"
)

None¶

criterion = HingeEmbeddingLoss(
    reduction="none"
)

Returns the loss for each element individually.

Typical Training Loop¶

criterion = HingeEmbeddingLoss()

loss = criterion(
    distances,
    labels
)

loss.backward()
optimizer.step()

Typical Applications¶

• Siamese neural networks
• Face verification
• Signature verification
• Metric learning
• Similarity learning
• Image retrieval

Notes¶

• Expects the target tensor to contain only 1 or -1.
• Input values typically represent distances or similarity scores between pairs of samples.
• Negative pairs are penalized only when their distance is smaller than the specified margin.
• Supports "mean", "sum", and "none" reductions.
• Commonly used for learning embedding spaces where similar samples are close together and dissimilar samples are separated by at least the margin.