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

arXiv: https://arxiv.org/abs/2605.11645 · HTML: https://mlsanity.com/paper/2605.11645/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Financial trading and forecasting agents, one of 16 directions in LLM agents and tool use.
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM agents and tool use / [Financial trading and forecasting agents](https://mlsanity.com/agents/financial-trading-and-forecasting-agents/)

## Builds on (most cited first, 11 of 11)

- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [FinCon: A Synthesized LLM Multi-Agent System with Conceptual Verbal Reinforcement for Enhanced Financial Decision Making](https://mlsanity.com/paper/2407.06567/) (2024)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [TwinMarket: A Scalable Behavioral and Social Simulation for Financial Markets](https://mlsanity.com/paper/2502.01506/) (2025)
- [Predicting discrete-time bifurcations with deep learning](https://mlsanity.com/paper/2303.09669/) (2023)
- [MASS: Muli-agent simulation scaling for portfolio construction](https://mlsanity.com/paper/2505.10278/) (2025)
- [Agent-Based Simulation of a Financial Market with Large Language Models](https://mlsanity.com/paper/2510.12189/) (2025)
- [Probing Dec-POMDP Reasoning in Cooperative MARL](https://mlsanity.com/paper/2602.20804/) (2026)
- [Stability of China's Stock Market: Measure and Forecast by Ricci Curvature on Network](https://mlsanity.com/paper/2204.06692/) (2022)
- [An Imbalance-Robust Evaluation Framework for Extreme Risk Forecasts](https://mlsanity.com/paper/2512.00916/) (2025)

## Abstract (arXiv)

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.