Effect of real transformer training dynamics on the impossibility result

Verify how complex gradient interactions and emergent behaviors in real transformer training that may resist simple decomposition affect the Impossibility Theorem that models large language model inference as an auction and derives the impossibility via the Green-Laffont framework. In particular, determine whether the theorem’s conclusions continue to hold under realistic training dynamics where components’ contributions to utility cannot be cleanly decomposed.

Background

The paper proves an Impossibility Theorem stating that no LLM inference mechanism can simultaneously satisfy truthfulness, semantic information conservation, relevant knowledge revelation, and knowledge-constrained optimality. The proof models inference as an auction of ideas and relies on mechanism design results, particularly the Green-Laffont theorem, under assumptions such as independently distributed private knowledge and quasilinear utilities.

The authors note that real transformer training involves complex gradient interactions and emergent behaviors which may not admit a simple decomposition of utilities across components. This raises uncertainty about whether the formal payment and utility structures required by the theorem strictly apply to practical training regimes, motivating verification of the theorem’s robustness under realistic dynamics.