171. Word2Vec Skip-gram with Negative Sampling

Implement the skip-gram loss with negative sampling used in Word2Vec.

Signature: def skipgram_loss(center_emb: np.ndarray, pos_emb: np.ndarray, neg_embs: np.ndarray) -> float

Inputs:

• center_emb: shape (d,) — embedding of the center word
• pos_emb: shape (d,) — embedding of a positive context word
• neg_embs: shape (k, d) — embeddings of k negative samples

Loss:

L = -log(sigmoid(center . pos)) - sum_i log(sigmoid(-center . neg_i))

Use a numerically stable log-sigmoid (do not call np.log(sigmoid(x)) directly).