# Sheaf-Inspired Structured Scoring Extensions of LightGCN for Collaborative Filtering

**Authors:** Ksenia Belkovskaya, Timur Lidzhiev, Maria Stebliy, Alexander Tarakanov  
**Published:** 12 Nov 2026  
**Links:** [arXiv](https://arxiv.org/abs/2611.17226) · [PDF](https://arxiv.org/pdf/2611.17226) · [This page](https://omen-bit.github.io/ai-paper-daily/paper/2611.17226.html)

## Abstract

Graph-based collaborative filtering learns user and item representations by propagating embeddings over a user--item interaction graph. We investigate a modular, sheaf-inspired scoring extension placed on top of a three-layer LightGCN backbone. The motivation comes from cellular sheaves, where local vector spaces are related by linear restriction maps; here, this idea motivates structured, pair-dependent transformations of user and item embeddings rather than a change to graph propagation. We compare the identity inner-product scorer, diagonal, rank-one low-rank, and full matrix residual scorers, and a parameter-matched residual MLP baseline (\texttt{mlp\_full}) on Amazon-Book, Gowalla, MovieLens-1M, and Yelp2018. We report ranking quality and catalog coverage at cutoffs 10 and 20. The selected structured variants show modest, dataset-dependent changes in ranking quality and sometimes substantial changes in coverage. Our method is inspired by sheaf geometry but does not construct a cellular sheaf or implement sheaf-Laplacian diffusion; the experiments therefore do not establish a causal benefit from sheaf geometry itself.

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