Behavioral Probes for Information Flow in LLM Swarms

Human swarm intelligence demonstrates remarkable collective accuracy but faces scalability constraints in cost, coordination, and time. We investigate whether large language models (LLMs) can approximate swarm intelligence effects through artificial swarms, addressing a critical gap in understanding AI-based aggregation mechanisms. We conducted a controlled experiment with 960 manually executed prompts across three proprietary models (GPT-5, Gemini 2.5 Pro, Claude Sonnet 4.5), testing intra-model sampling and inter-model aggregation on eight estimation tasks. Results reveal consistent error reduction through intra- and inter-model aggregation, with significant error reductions up to 37 percentage points in MAPE across different aggregation strategies. We observed small to large effect sizes for positive correlations (Spearman's $ρ=0.242-0.568$, all $p<0.001$) between relative confidence interval widths and relative estimation errors, suggesting LLMs possess metacognitive awareness when assessing uncertainty. We discuss implications for research and practice, providing actionable insights for deploying LLM swarms in organizational decision-making.

Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse observations, showing that it depends strongly on prompt text and query protocol. We introduce an uncertainty-alignment criterion that measures whether model uncertainty tracks residual ambiguity among sample-consistent functions. Across controlled inference tasks and Bayesian optimization studies, we find that structural prompts act as effective priors, POINTWISE and JOINT querying induce different beliefs, and sequential evidence leads to non-monotonic, order-sensitive confidence updates. These effects change downstream acquisition decisions and regret, showing that elicitation protocol is part of the LLM surrogate specification, not a formatting detail.

As LLM agents increasingly collaborate on complex tasks, how to organize their interactions becomes a central design question. Existing multi-agent systems typically learn or adapt explicit roles, hierarchies, routing policies, or communication topologies. We shift the learning target to a reusable local law that can be shared across interchangeable agents and adapt coordination as populations or interaction conditions change, without redefining a global organization. We introduce Waggle, a shared anonymous policy over bounded local views that jointly selects task actions, semantic communication, and local commitment updates. Repeated execution of the same law allows coordination to form, persist, and reorganize online without explicit roles or global topology. To learn this law across interchangeable agents and evolving coordination, we develop Swarm-Consistent Distillation (SCD), combining anonymous-orbit consistency with rollout-grounded prediction of the next local coordination field, with no added inference-time components. Across diverse coordination settings, the same learned law remains effective as populations and interaction budgets change, retains over 96% of substrate-specific oracle quality, and transfers without retraining; SCD further improves reorganization after counterevidence. Together, these results show that LLM-agent organization can emerge and adapt through repeated execution of a learned local law.