Match each contrastive loss to its defining mechanism

All four losses are in the broad contrastive-learning family. They all train embeddings so similar inputs get close and dissimilar ones get far apart. But each one uses a different mechanism to achieve that goal. **InfoNCE** treats the task as multiple-choice classification. Given a query and N candidates (one positive, N-1 negatives), the model has to pick the positive. The loss is cross-entropy over a softmax of similarity scores. This is the dominant choice for modern embedding training. **Triplet loss** works with triples: an anchor, a positive (related to the anchor), and a negative (unrelated). The loss says the anchor-positive distance must be smaller than the anchor-negative distance by at least a margin. If not, the model pays a penalty. It's older than InfoNCE and harder to scale. **MNRL (Multiple Negatives Ranking Loss)** is essentially InfoNCE with in-batch negatives: every other example in the batch counts as a negative for every example. No explicit negative mining required. This is the default in Sentence-Transformers. **Cosine embedding loss** is the regression-style sibling. Given pairs with known similarity labels (e.g. STS-B has graded similarity from 0 to 5), the model is trained to make `cos(u, v)` equal to a target value. Used when graded similarity data is available.

Four contrastive losses, four distinct mechanisms. **InfoNCE** is cross-entropy over a softmax of similarities. For a query and N candidates (1 positive + N-1 negatives), the loss is: $$\mathcal{L}_{\text{InfoNCE}} = -\log \frac{\exp(\text{sim}(q, k^+) / \tau)}{\sum_i \exp(\text{sim}(q, k_i) / \tau)}$$ The positive is the "correct class" among N candidates. Modern frontier embedding models (OpenAI text-embedding-3, Voyage v3, BGE-M3) all use InfoNCE or close variants. **Triplet loss** is the margin-based formulation. For an anchor `a`, positive `p`, negative `n` and margin `m`: $$\mathcal{L}_{\text{triplet}} = \max(0, \text{sim}(a, n) - \text{sim}(a, p) + m)$$ The loss is zero when the positive is at least `m` more similar than the negative, otherwise it's positive. Only one negative per triplet, so the gradient signal is bounded. Used in FaceNet and metric-learning settings. **MNRL** (Multiple Negatives Ranking Loss) is InfoNCE applied to in-batch negatives. Every other example in the batch serves as a negative. It's the default loss in Sentence-Transformers and is the simplest way to fine-tune a custom embedding model: no explicit negative mining required. **Cosine embedding loss** is a regression-style loss for graded similarity. If your training data has pairs with continuous similarity labels (STS-B style), this loss directly fits `cos(u, v)` to the target value. Used in multi-task setups alongside InfoNCE for similarity calibration.