Notes

MLP Recommender

Matrix factorization decides how much a user will like an item with one fixed operation: multiply two vectors element by element and add up the result. That arithmetic is the entire model. An MLP recommender asks what happens if you let a network learn that final step instead of prescribing it.

How it works
The user id and item id each index into an embedding table. The two embeddings are concatenated rather than multiplied, and the result is pushed through a stack of fully connected layers with non-linear activations, narrowing to a single output read as the probability of interaction. Training uses implicit feedback: observed interactions are positives, items sampled from the catalogue are negatives, and the loss is binary cross-entropy. This is the MLP path of Neural Collaborative Filtering — the half that NeuMF fuses with a factorization path.

What it buys
Concatenation plus hidden layers can represent interactions no inner product can express: a user who likes a genre only in short formats, a pairing that works at breakfast and nowhere else. The network discovers those shapes from data instead of having them hand-engineered as features.

Where it has to sit
An MLP score cannot be resolved by a vector index, because there is no dot product to search — every candidate needs its own forward pass. That rules it out of retrieval over millions of items and places it firmly in the ranking stage, scoring the few thousand candidates an earlier stage already narrowed. On MovieLens-scale benchmarks its advantage over a well-tuned factorization model is also smaller than its first results suggested, so it earns its place by what it can express, not by headline accuracy.

An MLP recommender scores a user-item pair by concatenating their learned embeddings and passing the result through fully connected layers, letting the network learn the interaction function instead of fixing it as an inner product. It is the neural path of Neural Collaborative Filtering, trained on implicit feedback with sampled negatives. Because every candidate needs its own forward pass, it belongs in the ranking stage rather than in retrieval.

Imagine two shop assistants. The first follows a fixed rule: score how well your tastes line up with the product’s qualities, add it up, done. The second is allowed to form a judgement any way they like after looking at both.

An MLP recommender is the second assistant. The software still describes you and each item as lists of numbers, but instead of combining them with one set formula, it feeds both into a small learning network that works out its own way of deciding. The hope is that it catches quirks a rigid formula misses — the fact that you like cookbooks, but never on a weekday.