GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulations

2026-05-12

AI Summary

This study addresses the lag inherent in traditional price-correlation-based measures of herding behavior, which impedes timely systemic risk预警. The authors propose a novel, forward-looking geometric framework that introduces discrete Ollivier–Ricci curvature—hitherto unexplored in finance—to predict herding dynamics. By constructing an agent interaction graph to capture the topological structure of coordinated behavior and leveraging a large language model–driven multi-agent simulator to generate upstream behavioral data, the approach bridges geometry and finance. Theoretically, the work establishes a mean-field connection between graph curvature and the classical CSAD statistic. Empirically, in both continuous-spin and Vicsek models, the primary detector anticipates herding events by an average of 272 steps, while the contagion detector recalls 65% of critical trajectories 318 steps in advance. Notably, curvature signals lead conventional price-correlation baselines by 40 steps, and the effective action vocabulary contracts significantly during cascades.

Abstract

Herding -- where agents align their behaviors and act collectively -- is a central driver of market fragility and systemic risk. Existing approaches to quantify herding rely on price-correlation statistics, which inherently lag because they only detect coordination after it has already moved realised returns. We propose GeomHerd, a forward-looking geometric framework that bypasses this observability lag by quantifying coordination directly on upstream agent-interaction graphs. To generate these graphs, we treat a heterogeneous LLM-driven multi-agent simulator -- each financial trader instantiated by a persona-conditioned LLM call -- as a forecastable world, and evaluate the geometric pipeline on the Cividino--Sornette continuous-spin agent-based substrate as our headline financial testbed. By tracking the discrete Ollivier--Ricci curvature of these action graphs, GeomHerd captures the structural topology of emerging coordination. Theoretically, we establish a mean-field bridge mapping our graph-theoretic metric to CSAD, the classical macroscopic herding statistic, linking GeomHerd to downstream price-dispersion measurement. Empirically, GeomHerd anticipates herding long before aggregate market baselines: on the continuous-spin substrate, our primary detector fires a median of 272 steps before order-parameter onset; a contagion detector ($β_{-}$) recalls 65% of critical trajectories 318 steps early; and on co-firing trajectories the agent-graph signal precedes price-correlation-graph baselines by 40 steps. As a complementary indicator, the effective vocabulary of agent actions contracts during cascades. The geometric signature transfers out-of-domain to the Vicsek self-driven-particle model, and a curvature-conditioned forecasting head reduces cascade-window log-return MAE over detector-conditioned and price-only baselines.

Problem

• herding
• market fragility
• systemic risk
• observability lag
• agent coordination

Innovation

• Ricci curvature
• herding detection
• multi-agent simulation
• LLM-driven agents
• geometric forecasting