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This paper investigates the emergence of popularity bias in recommendation systems by modeling the interaction dynamics between user engagement and recommender model updates through a dynamical systems framework. Using a stochastic process and ordinary differential equations, the authors derive conditions for the emergence of popularity bias and the potential for equitable user retention. Experimental validation on both synthetic data and real-world music recommendation logs confirms the theoretical findings, highlighting the critical balance needed to maintain diverse user engagement.
Popularity bias can be mathematically characterized, revealing conditions that allow for equitable user retention in recommendation systems.
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.
