172. InfoNCE Contrastive Loss

Implement the InfoNCE contrastive loss for a single query against one positive and several negatives.

Signature: def info_nce(query: np.ndarray, positives: np.ndarray, negatives: np.ndarray, tau: float = 0.07) -> float

Inputs (assume already L2-normalized — do not renormalize):

• query: shape (d,)
• positives: shape (d,) — a single positive key
• negatives: shape (n, d)

Logits:

• logit_pos = (query . positives) / tau
• logits_neg[i] = (negatives[i] . query) / tau

Loss: -logit_pos + log(exp(logit_pos) + sum(exp(logits_neg)))

Use log-sum-exp for stability.