Stretch: Triplet Loss (Metric/Representation Learning)

The problem, from first principles

06-info-nce-loss compares one anchor against many candidates at once (an entire batch). Triplet loss asks the simplest possible version of the same underlying question, using just three examples at a time: given an anchor, a "positive" example that should be similar to it, and a "negative" example that should be dissimilar, push the anchor closer to its positive than to its negative, by at least some margin. It doesn't care about absolute distances at all — only the relative ordering, which is exactly what makes it useful for learning an embedding space with no fixed set of classes (face recognition being the classic example: there's no finite list of "face classes," only "same person" vs. "different person" comparisons).

From theory to code

Theory says: for each anchor/positive/negative triplet, compute the anchor's distance to its positive and its distance to its negative. If the negative is already farther away than the positive by at least margin, that triplet contributes nothing (loss 0) — the model already has it right, with room to spare. Otherwise, the loss is exactly how far short of that margin the triplet currently falls.

Implement triplet_loss(anchor, positive, negative, margin=1.0) against that reasoning.

Constraints

• anchor, positive, negative: all shape (N, D) — row i across the three arrays forms one triplet.
• margin: a positive float, the minimum required gap between the two distances.
• Returns a single Python float: the mean per-triplet loss across all N triplets.
• None of the three inputs are modified in place.

Hints

Open one at a time. Each gives away a little more than the last.