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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.11645 |
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| _version_ | 1866911673256771584 |
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| author | Yang, Lake Su, Junwei Zeng, Jingfeng Lu, Wenhao Qian, Xingzhi Zhang, Weitong Wu, Chuan Jin, Dunhong |
| author_facet | Yang, Lake Su, Junwei Zeng, Jingfeng Lu, Wenhao Qian, Xingzhi Zhang, Weitong Wu, Chuan Jin, Dunhong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11645 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulations Yang, Lake Su, Junwei Zeng, Jingfeng Lu, Wenhao Qian, Xingzhi Zhang, Weitong Wu, Chuan Jin, Dunhong Multiagent Systems Machine Learning Statistical Finance 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. |
| title | GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulations |
| topic | Multiagent Systems Machine Learning Statistical Finance |
| url | https://arxiv.org/abs/2605.11645 |