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

Paper: arXiv 2605.11645

Authors: Lake Yang, Junwei Su, Jingfeng Zeng, Wenhao Lu, Xingzhi Qian, Weitong Zhang, Chuan Wu, Dunhong Jin

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10 (capped from 8.0: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The research introduces advanced differential geometry (Ollivier-Ricci curvature, Wassertein distance, Ricci flow) alongside a rigorous, multi-factor empirical evaluation using LLM-driven agent-based simulations and statistical validation against classical metrics like CSAD and LSV.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Detect Market Herding <br/>via Forward-looking Geometry] --> B[<b>Inputs:</b> LLM-driven Multi-agent<br/>Simulations & Agent Graphs]
    B --> C[<b>Process:</b> Compute Discrete<br/>Ollivier-Ricci Curvature]
    C --> D[<b>Theory:</b> Mean-field bridge<br/>to classical CSAD metric]
    D --> E[<b>Outcomes:</b> Early detection (272+ steps)<br/>of cascades & Reduced MAE]
    E --> F[<b>Generalization:</b> Transferable to<br/>Vicsek/Other Domains]

Cited References (44)

1. A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades (1992)
2. A simple model of herd behavior (1992)
3. Multidimensional Uncertainty and Herd Behavior in Financial Markets (1998)
4. Herd Behavior and Investment (1990)
5. Herd Behavior in Financial Markets (2001)
6. Financial Contagion (2000) — link
7. Systemic Risk and Stability in Financial Networks (2015) — link
8. Financial Networks and Contagion (2014) — link

2 of 44 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.