Measuring Emergent Coordination in Multi-Agent LLMs via Information Decomposition

Group binary search Illustrative

Each agent guesses 0–50; guesses must sum to a hidden target. Only "too high / too low" is shared. Target 237 is chosen here for illustration.

Why identical agents fail

Identical guesses give sums that are multiples of 10. Complementary offsets are needed for other targets.

Partial information decomposition

Information that sources X1, X2 carry about target Y splits into four atoms. Textbook examples

Which redundancy definition?

Synergy depends on the chosen redundancy measure.

Three prompt conditions

Click a layer stack. The clean ToM effect is ToM vs Persona.

Three instruments on short trajectories

Null baselines Reported design

Score = observed − median of shuffled scores. Click a stage.

Preliminary experiment: 7,150 runs Reported

Odds ratios for success (log axis). No intervals reported in the discussion.

Reported results Reported

Significance heatmap (−log10 p)

Hover a cell. Colour scales −log10 p, capped at 16.

Pooled signal vs. individual groups

200 groups. Reported: 3.5% clear p<0.05 alone; chance gives about 5% (~10). Which groups is not reported. Illustrative layout

Two questions, two tests Illustrative

Link to performance Reported

Synergy × redundancy interaction: β 0.24, p 0.014 (27% log-odds amplification). Mediation of ToM → success via synergy:

Controls the discussion would want Suggested, not in paper