# Geometric Collaborative Filtering with Convergence

arXiv: https://arxiv.org/abs/2410.03064 · HTML: https://mlsanity.com/paper/2410.03064/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 22 of 22)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Are We Really Making Much Progress? A Worrying Analysis of Recent Neural Recommendation Approaches](https://mlsanity.com/paper/1907.06902/) (2019)
- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)
- [Neural Collaborative Filtering vs. Matrix Factorization Revisited](https://mlsanity.com/paper/2005.09683/) (2020)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [Warm Up Cold-start Advertisements: Improving CTR Predictions via Learning to Learn ID Embeddings](https://mlsanity.com/paper/1904.11547/) (2019)
- [RecVAE: a New Variational Autoencoder for Top-N Recommendations with Implicit Feedback](https://mlsanity.com/paper/1912.11160/) (2019)
- [Neural Network Matrix Factorization](https://mlsanity.com/paper/1511.06443/) (2015)
- [Revisiting the Performance of iALS on Item Recommendation Benchmarks](https://mlsanity.com/paper/2110.14037/) (2021)
- [Intrinsic Dimension Estimation Using Wasserstein Distances](https://mlsanity.com/paper/2106.04018/) (2021)
- [Rethinking Collaborative Metric Learning: Toward an Efficient Alternative without Negative Sampling](https://mlsanity.com/paper/2206.11549/) (2022)
- [Alleviating Cold-start Problem in CTR Prediction with A Variational Embedding Learning Framework](https://mlsanity.com/paper/2201.10980/) (2022)
- [The Minority Matters: A Diversity-Promoting Collaborative Metric Learning Algorithm](https://mlsanity.com/paper/2209.15292/) (2022)
- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [Enhancing VAEs for Collaborative Filtering: Flexible Priors & Gating Mechanisms](https://mlsanity.com/paper/1911.00936/) (2019)
- [Deep Variational Autoencoder with Shallow Parallel Path for Top-N Recommendation (VASP)](https://mlsanity.com/paper/2102.05774/) (2021)
- [MARec: Metadata Alignment for cold-start Recommendation](https://mlsanity.com/paper/2404.13298/) (2024)

## Built on by (most cited first, 1 of 1)

- [On the Mechanisms of Collaborative Learning in VAE Recommenders](https://mlsanity.com/paper/2511.06781/) (2025)

## Abstract (arXiv)

Latent variable collaborative filtering methods have been a standard approach to modelling user-click interactions due to their simplicity and effectiveness. However, there is limited work on analyzing the mathematical properties of these methods in particular on preventing the overfitting towards the identity, and such methods typically utilize loss functions that overlook the geometry between items. In this work, we introduce a notion of generalization gap in collaborative filtering and analyze this with respect to latent collaborative filtering models. We present a geometric upper bound that gives rise to loss functions, and a way to meaningfully utilize the geometry of item-metadata to improve recommendations. We show how these losses can be minimized and gives the recipe to a new latent collaborative filtering algorithm, which we refer to as GeoCF, due to the geometric nature of our results. We then show experimentally that our proposed GeoCF algorithm can outperform other all existing methods on the Movielens20M and Netflix datasets, as well as two large-scale internal datasets. In summary, our work proposes a theoretically sound method which paves a way to better understand generalization of collaborative filtering at large.