I'm building product recommendations from user embeddings and item vectors

Great — a standard setup for recommendation systems.

At a high level, if you have:

• a user embedding (u \in \mathbb{R}^d)
• an item vector (v_i \in \mathbb{R}^d)

then the simplest recommendation score is usually:

[ \text{score}(u, v_i) = u^\top v_i ]

Higher dot product = more relevant item.

Common ways to use user/item embeddings

1) Dot product ranking

• Compute scores for all candidate items
• Rank descending
• Works well if embeddings were trained to make dot product meaningful

2) Cosine similarity

[ \frac{u^\top v_i}{|u||v_i|} ] Useful if vector norms should not affect ranking.

3) Two-tower retrieval

If your embeddings come from a two-tower model:

• user tower produces user vector
• item tower produces item vector
• train with sampled negatives / in-batch negatives
• retrieve nearest items with ANN search

4) Feed embeddings into a downstream ranker

Use:

• dot product
• elementwise product
• absolute difference
• concatenation
• metadata features

Then train a learned ranking model.

Practical recommendation pipeline

1. Precompute all item vectors.
2. Encode each user request into a user embedding.
3. Score items by dot product or ANN similarity.
4. Filter unavailable items.
5. Optionally rerank top-K with a richer model.

Important considerations

• Normalization: if you use dot product, vector norms matter a lot.
• Negative sampling: crucial if training embeddings.
• Cold start: new users/items need content features or defaults.
• Latency: ANN indexes like FAISS, ScaNN, or HNSW are often needed for large catalogs.
• Evaluation: use Recall@K, NDCG@K, MAP, hit rate, and offline/online A/B tests.

If you want, I can help with any of these next:

• designing the scoring function
• training objective for embeddings
• FAISS / ANN retrieval
• Python code for recommendations
• handling cold start and ranking metrics