GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulations
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.
Large language models (LLMs) are being deployed at scale in consequential real-world systems, from financial markets to content moderation to hiring. We show that improving individual model capability can degrade rather than improve system-level outcomes. We hypothesize that shared training and architectures can lead more capable LLMs to behave more similarly, creating correlated actions that do not diversify away. We develop a general framework showing how this correlation creates a non-diversifiable risk floor and test its predictions in financial markets using an agent-based simulation with LLM traders of varying general-purpose capability. We find that: (1) frontier LLMs exhibit significantly correlated behavior that increases with capability; (2) when their shared reasoning is accurate, increasing agent participation reduces market-level risk; and (3) when agents share a common misinformation environment, the same correlated behavior becomes a liability. Together, these results identify a capability paradox: improving individual models does not necessarily produce better system-level outcomes. Whether the same dynamics arise in other domains is an open empirical question.
We report a pre-registered, two-part experiment on small economies of frontier language-model agents (Claude Opus 4.8), testing two quantitative predictions about coupled multi-agent systems: an information-theoretic capacity region for wealth growth under market coupling, and a mean-field residual-scaling law for population misalignment under incentive and control levers. All predictions, acceptance bands, and decision rules were frozen in a public git chain before any run; every reported number re-derives mechanically from cached model outputs; the entire experiment cost $138.76 in metered API spend and is re-runnable at zero cost from the cache. Result 1 (confirmation): in parimutuel-coupled economies, relative growth equals relative claimed information -- the gap law G_a - G_b = I_a - I_b holds to a worst-case 46 millinats (pre-registered band: 50) across four perception structures; coalition value is submodular exactly where channels are conditionally independent, and a designed XOR synergy control flips it supermodular by 0.62 >= ln2/2 nats, with agents reasoning out the joint bit; the joint growth ceiling G_S <= H(X) binds exactly; and the best-informed agent absorbs essentially the whole wealth pool in 4/5 market seeds. Result 2 (structural negative): the residual-scaling test returned "domain not found." In all 72 population runs, goal dispersion collapsed (V -> 0; maximum 4.85 against a frozen floor of 5.31), the population's response to the two levers was a step function across the dominance boundary rather than a smooth response, and cells near the boundary were bistable with seed-selected outcomes. No tested LLM population at any capability level realizes the noise-maintained-dispersion regime the smooth mean-field model assumes. We release the full protocol, pre-registration chain, call cache, and analysis code.
Transaction-local controls answer whether one financial request may proceed, but market behavior can be distributed across messages, agents, assets, and time. We study this interpretation gap in a virtual exchange populated by ten role-conditioned language-model agents. The agents communicate, trade reference assets and futures, launch tokens, and manage concentrated-liquidity pools under prescriptive adversarial roles. We analyze eight 72-cycle trajectories across two time-blinded hourly replay paths, with a runner-side wallet policy enabled or disabled. The retained artifacts connect generated outgoing messages, policy events, balances, positions, and cycle-end market state. A focal reconstruction shows a launch--promotion--exit scenario realized across private coordination, public claims, follower positioning, repeatedly withheld exits, and a later non-blocking request aligned with a token balance change. Across policy-enabled runs, the gate withholds direct requests selectively; most policy-categorized candidates are flagged rather than blocked, while the surrounding interaction can continue. Repeated runs also show that category-level and within-trajectory relations can recur even when normalized score-change rankings do not. These findings motivate agent-behavior evaluation that links communication, authorization, and evolving state instead of treating individual transaction verdicts as complete safety judgments.