Multi-Head Attention Is a Multi-Player Game

TL;DR

This paper models transformer attention heads as players in a game, analyzes how their interactions affect training efficiency, and proposes regularization methods to improve performance and reduce hallucinations.

Contribution

It formalizes the multi-head attention as a potential game, derives bounds on inefficiency, and introduces GAME-LoRA to improve training outcomes by reducing head redundancy.

Findings

PoA bound predicts hallucination likelihood

Emergent coalitions show selective coordination

GAME-LoRA reduces hallucinations by up to 18%

Abstract

Modern transformer attention is internally multi-agent -- heads compete and coordinate -- yet we train it as if it were a monolithic optimizer. We formalize this gap: cross-entropy training induces an implicit potential game among heads, and gradient descent converges to Nash equilibria with potentially unbounded inefficiency due to unpriced externalities (redundancy, correlated errors). Our main result bounds the Price of Anarchy by $\Gamma(G)$, the off-diagonal mass of a head interaction matrix capturing weight and gradient coupling. Under mild smoothness assumptions, we prove that both \emph{excess hallucination probability} and \emph{excess head redundancy} scale with PoA, unifying two distinct failure modes into a single mechanism. The bound is prescriptive: regularization that reduces $\Gamma(G)$ provably tightens PoA. We instantiate this as GAME-LoRA, combining Barlow Twins decorrelation with log-determinant coordination pressure. Experiments validate the theory: $\Gamma(G)$ predicts hallucination ($p{<}0.05$), emergent coalitions exhibit selective coordination, and GAME-LoRA achieves up to 18\% hallucination reduction (8\% average) with no knowledge degradation -- a Pareto improvement inaccessible to methods ignoring the game structure.