Neural Collaborative Filtering: Learning Non-Linear User-Item Preferences

Training

Hidden units 4

Learning rate 0.50

Explore a viewer

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Live Metrics

Epoch

Accuracy

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BCE loss

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Top score

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How it works

Classic matrix factorization predicts a rating as a plain dot product p_u·q_i of a user embedding and an item embedding — a linear model. Neural Collaborative Filtering (He et al., 2017) replaces that dot product with a small neural network that can learn a non-linear interaction function instead:

x = [p_u ; q_i]                (concat, 6-dim)
z1 = W1·x + b1 ;  h = ReLU(z1)   (hidden layer)
z2 = W2·h + b2 ;  ŷ = σ(z2)      (predicted score, 0-1)
loss = −Σ [y·log ŷ + (1−y)·log(1−ŷ)]   (binary cross-entropy)

Every training step runs full-batch gradient descent: it backpropagates the loss through the output, the hidden layer, and all the way into the embeddings themselves — so p_u and q_i are learned jointly with the network weights, not fixed in advance. That is why the spheres on the left visibly drift during training: the model is reshaping the latent space so that a viewer's point ends up close, in this learned geometry, to the movies their network activations predict they'll like.

Hidden units — width of the interaction layer; more units can fit sharper non-linear boundaries between genres, at the cost of needing more data.
Learning rate — step size of each gradient-descent update.
Explore a viewer — draws a live line from that viewer to every movie, brightness set by the model's current predicted score ŷ.

This toy catalogue is small and dense enough to train on every pair each epoch; production recommenders (YouTube's deep ranking model, for example) face millions of items and instead train on sampled negatives, but the underlying embed-then-interact math is the same.

Viewers Movies Hidden-layer units

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