GeomHerd uses Ricci curvature to predict financial herding 272 steps early

Traditional herding detection relies on price correlations—metrics that only flag coordination after it has already moved markets. GeomHerd bypasses this lag by measuring the structural topology of agent interactions in real time. The system uses an LLM-powered multi-agent simulator where each trader is an LLM with a persona, generating an action graph over discrete time steps. By tracking the discrete Ollivier-Ricci curvature of this graph, GeomHerd captures emerging coordination patterns before they manifest in aggregate price data. The researchers also establish a theoretical bridge connecting their graph-based metric to the classic CSAD herding statistic.

Empirically, GeomHerd fires its primary detector a median of 272 steps before order-parameter onset on the Cividino–Sornette spin model. A contagion detector (β−) recalls 65% of critical trajectories 318 steps early. On co-firing trajectories, the agent-graph signal precedes price-correlation-graph baselines by 40 steps. The method transfers out-of-domain to the Vicsek self-driven-particle model, and a curvature-conditioned forecasting head reduces cascade-window log-return MAE by a significant margin over baselines. This geometric approach offers a forward-looking alternative to reactive market fragility indicators.