LightGCN
Graph recommenders borrowed their machinery from graph convolution over node-feature graphs, and then someone checked which parts were earning their keep on a user-item graph. The answer was: almost none of them. LightGCN is what was left after that ablation.
What was removed
NGCF inherited feature-transformation matrices and nonlinear activations from standard graph convolution. LightGCN drops both. A layer does nothing but average a node's neighbours' embeddings, normalised by the square root of both degrees, and the only trainable parameters in the whole model are the layer-zero user and item embeddings. The final representation is a weighted sum of every layer's output, the score is a plain dot product, and training uses the BPR pairwise loss on sampled negatives.
Why stripping it down works
The interaction graph carries no node features — an id is not a feature — so a transformation matrix has nothing to transform and only adds parameters that overfit sparse data. What remains, propagation, is the part that matters: after two or three layers a user's embedding has absorbed signal from the items of users who overlap with them, which is collaborative filtering expressed as smoothing over the graph. Summing all layers rather than taking the last is what keeps that smoothing from collapsing every embedding together.
What it costs
Propagation is a sparse matrix multiply over the whole graph, once per layer per epoch, so training scales with the number of interactions. Serving is cheap: propagated vectors are precomputed and retrieval is nearest-neighbour search in an index such as FAISS. A new user or item has no position in the graph until it interacts, so cold start is untouched.
LightGCN is a graph-based recommender that keeps only neighbourhood propagation over the user-item bipartite graph, discarding the feature transformations and nonlinear activations NGCF inherited from general graph convolution. Its only parameters are the base user and item embeddings; scores are dot products trained with the BPR loss. On id-only interaction data the stripped-down form trains faster and generalises better, which made it the standard graph baseline.
Word of mouth spreads in steps. A friend's recommendation reaches you, and so, a little more faintly, does their friend's. LightGCN works that way: it treats people and items as one big web of connections and lets preference travel along it.
Each round, a person's profile is nudged toward the things they engaged with, and each thing is nudged toward the people who engaged with it. Repeat that two or three times and you start picking up signal from people you share nothing direct with. The light in the name is the point — its authors found most of the complicated machinery in earlier versions could simply be deleted, and the simpler model worked better.