Contrastive loss for a pair of embeddings

Pull similar pairs together and push dissimilar pairs apart

Metric learning trains an embedding so that the distance between two inputs matches whether they are the same. The contrastive loss (Hadsell, Chopra and LeCun, 2006) scores one pair given its distance d and a flag s (1 for similar, 0 for dissimilar):

L = s * d^2 + (1 - s) * max(0, m - d)^2

Similar pairs are penalized by their distance. Dissimilar pairs are penalized only while they sit inside the margin m.

Implement contrastive_loss(distances, is_similar, margin=1.0), which applies the formula elementwise.

• distances and is_similar have the same shape. is_similar holds 0 or 1 values.
• Return an array of the same shape.

Constraints

• Shapes must match. Otherwise raise ValueError.
• Any negative distance raises ValueError.
• margin < 0 raises ValueError.
• is_similar values other than 0 and 1 raise ValueError.
• Do not modify the inputs.

Hints