Stay or Stray - A Dynamical Systems Viewpoint of Popularity Bias

2026-08-11

AI Summary

This work addresses the prevalence bias in recommender systems caused by data overload from mainstream user interactions, which undermines recommendation fairness for niche users. It pioneers a dynamical systems perspective to model the coupled evolution of recommendation model updates and user behavior, establishing an ordinary differential equation (ODE) framework grounded in two-timescale stochastic approximation theory. This framework rigorously characterizes the emergence mechanism of popularity bias and derives precise theoretical conditions under which such bias inevitably arises or, conversely, under which preferences of all user groups can be fairly preserved. Empirical validation on both synthetic data and real-world logs from a large-scale commercial music recommendation platform confirms the theoretical predictions, revealing the dynamic processes driving popularity bias formation and identifying viable pathways for its mitigation.

Abstract

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.

Problem

• popularity bias
• recommendation systems
• user engagement
• dynamical systems
• niche users

Innovation

• dynamical systems
• popularity bias
• two-time-scale stochastic approximation
• ODE framework
• recommender systems