Matrix factorization predicts how much a user will like an item by taking the dot product of their two learned vectors. That dot product is a fixed, linear way of combining them. In a 2017 paper presented at the Web Conference (WWW 2017), Xiangnan He and colleagues argued that this fixed interaction limits the model, and proposed Neural Collaborative Filtering (NCF) to learn the interaction function from data instead.
NCF keeps the idea of learning an embedding vector for each user and each item, but feeds those vectors into a neural network, a multi-layer perceptron, that can in principle learn any function of them rather than only their dot product. The authors also presented a combined model, Neural Matrix Factorization, that fuses a linear factorization component with the neural component to capture both simple and complex interaction patterns. Focusing on implicit feedback such as clicks and purchases, they reported improvements over strong baselines on benchmark datasets.
The paper became one of the most cited and most debated works in modern recommendation. It was influential in pushing deep learning into collaborative filtering, though later analyses questioned whether the neural interaction reliably beats a well-tuned dot product, a useful reminder that careful baselines matter.
For a general reader, this paper marks the point where the recommendation field seriously tried to replace a simple formula with a learned neural network, opening both new capability and a long argument about when the added complexity actually pays off.