Emergent Coordination in Multi-Agent LLMs

Framework: outcome-relevant PID over time. Three diagnostics: Practical criterion: does the macro signal at t predict the macro at t+ℓ beyond any single agent? Positive values indicate dynamical synergy. Emergence capacity: pairwise PID synergy for predicting future joint states, capturing “only-together” information that no single agent has. Coalition test: triplet info I3 vs. best pair (G3) to check if coalitions carry extra, goal-relevant predictability.

Experiment: group guessing without communication. Agents guess integers 0–50; only “too high/low” is returned to the whole group. Conditions: Plain, Persona, and Persona + ToM (“think about what others might do”).

Key findings for GPT-4.1: Emergence is real and steerable. Both the practical criterion and emergence capacity are >0 across conditions with robustness checks, indicating dynamical synergy. Personas induce stable, identity-linked differentiation; adding ToM increases alignment on the shared goal while keeping complementarity. Triplet structure matters. Many groups show G3>0, meaning no pair suffices; whole triplets add predictive information about the macro signal. ToM has higher total mutual information I3 (stronger shared-goal alignment) and more groups with significant I3. Performance emerges from balance. Synergy alone or redundancy alone does not predict success; their interaction does. Redundancy amplifies synergy’s effect and vice versa, consistent with integration + differentiation as the winning regime. Mediation suggests ToM boosts success indirectly by increasing synergy.

Lower-capacity model contrast (Llama-3.1-8B): Groups mostly fail; behavior shows strong temporal oscillations (time coupling) but weak cross-agent complementarity. ToM even hurts vs. Plain here, underscoring that ToM-style prompting needs sufficient model capacity.

Practical takeaways for AI devs: Design for complementary roles and shared target signals. Use light personas to stabilize identity-linked behaviors; add ToM-style reasoning to nudge agents to adapt to each other while aligning to the macro objective. Measure, don’t guess. Track macro predictability (practical criterion), pairwise synergy (capacity), and coalition additivity (G3) to diagnose when your team is a real collective vs. synchronized oscillators. Beware spurious emergence. Use row-shuffle (break identities) and column-shuffle (break cross-agent alignment) nulls to separate good synergy from mere temporal couplings.

Practical criterion: does the macro signal at t predict the macro at t+ℓ beyond any single agent? Positive values indicate dynamical synergy.

Emergence capacity: pairwise PID synergy for predicting future joint states, capturing “only-together” information that no single agent has.

Coalition test: triplet info I3 vs. best pair (G3) to check if coalitions carry extra, goal-relevant predictability.

Emergence is real and steerable. Both the practical criterion and emergence capacity are >0 across conditions with robustness checks, indicating dynamical synergy. Personas induce stable, identity-linked differentiation; adding ToM increases alignment on the shared goal while keeping complementarity.

Triplet structure matters. Many groups show G3>0, meaning no pair suffices; whole triplets add predictive information about the macro signal. ToM has higher total mutual information I3 (stronger shared-goal alignment) and more groups with significant I3.

Performance emerges from balance. Synergy alone or redundancy alone does not predict success; their interaction does. Redundancy amplifies synergy’s effect and vice versa, consistent with integration + differentiation as the winning regime. Mediation suggests ToM boosts success indirectly by increasing synergy.

Design for complementary roles and shared target signals. Use light personas to stabilize identity-linked behaviors; add ToM-style reasoning to nudge agents to adapt to each other while aligning to the macro objective.

Measure, don’t guess. Track macro predictability (practical criterion), pairwise synergy (capacity), and coalition additivity (G3) to diagnose when your team is a real collective vs. synchronized oscillators.

Beware spurious emergence. Use row-shuffle (break identities) and column-shuffle (break cross-agent alignment) nulls to separate good synergy from mere temporal couplings.