# Stay or Stray - A Dynamical Systems Viewpoint of Popularity Bias

arXiv: https://arxiv.org/abs/2608.10474 · HTML: https://mlsanity.com/paper/2608.10474/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Causal Intervention for Leveraging Popularity Bias in Recommendation](https://mlsanity.com/paper/2105.06067/) (2021)
- [Managing Popularity Bias in Recommender Systems with Personalized Re-ranking](https://mlsanity.com/paper/1901.07555/) (2019)
- [A Survey on Popularity Bias in Recommender Systems](https://mlsanity.com/paper/2308.01118/) (2023)
- [FairBalance: How to Achieve Equalized Odds With Data Pre-processing](https://mlsanity.com/paper/2107.08310/) (2021)
- [Algorithmic Drift: A Simulation Framework to Study the Effects of Recommender Systems on User Preferences](https://mlsanity.com/paper/2409.16478/) (2024)
- [Correcting Popularity Bias in Recommender Systems via Item Loss Equalization](https://mlsanity.com/paper/2410.04830/) (2024)
- [On Inherited Popularity Bias in Cold-Start Item Recommendation](https://mlsanity.com/paper/2510.11402/) (2025)

## Abstract (arXiv)

Popularity bias in recommendation systems arises when a majority user class generates disproportionate interaction data, causing the system to increasingly favour it while degrading recommendation quality for niche users. While extensive empirical evidence of popularity bias exists, the dynamics leading to its emergence are not well understood. In this work, we study the coupled evolution of recommender model updates and user engagement through the lens of dynamical systems. We formulate a stochastic process and analyse its asymptotic behaviour through an ordinary differential equation (ODE) framework grounded in two-time-scale stochastic approximation. We characterise the equilibrium points of this dynamical system, and derive conditions under which popularity bias is provably emergent, as well as conditions under which symmetric retention of all user classes is possible. We conduct experiments on synthetic data and real-world production logs derived from a large-scale commercial music recommendation platform to validate our theoretical results.