Opinion Leader Dynamics: How Sparse Attention Shapes Token Clustering

Sparse attention reduces the quadratic cost of global self-attention while retaining strong empirical performance, but how its restricted interactions shape the evolution of token representations remains theoretically underexplored. Modeling tokens as particles on the unit sphere, we introduce **opinion leader dynamics**, a framework that identifies two mechanisms through which token groups converge internally while maintaining distinct limiting directions. In the explicit model, fixed representatives induce a potential that attracts tokens toward distinct local maxima. In the implicit model, disconnected interaction groups evolve toward separate consensus directions. We formulate both models as *reverse Wasserstein gradient flows* and establish exponential convergence under suitable conditions. We further connect these theoretical predictions to token evolution in frontier sparse-attention LLMs that motivate our framework. Across four benchmarks, \\textcolor{#5178a1}{\\textbf{Kimi-K3}}, \\textcolor{#b11f23}{\\textbf{MiniMax-M3}}, and \\textcolor{#5178a1}{\\textbf{DeepSeek-}}\\textcolor{#b11f23}{\\textbf{V4-Flash}} consistently exhibit clearer cluster separation and higher clustering scores than the dense-attention model \\textcolor{#148e6f}{\\textbf{GLM-4.7-Flash}} in projected token representations. These observations support the relevance of the predicted multiple-group structure to trained frontier LLMs, while finite-particle simulations illustrate the theoretical convergence behavior. Together, our results connect restricted token interactions to distinct group-level attractors, providing a dynamical account of how sparse attention can support alignment within groups while preserving separation between them.