BAR Conjecture: the Feasibility of Inference Budget-Constrained LLM Services with Authenticity and Reasoning

TL;DR

This paper investigates the inherent trade-offs in designing large language model (LLM) services, demonstrating that optimizing for inference budget, authenticity, and reasoning capacity simultaneously is impossible, and introduces a formal framework to guide design choices.

Contribution

The paper formally proves the trade-off among inference budget, authenticity, and reasoning in LLMs and introduces the BAR Theorem framework for principled application design.

Findings

No model can optimize all three properties simultaneously.

Formal proof of the trade-off among inference budget, authenticity, and reasoning.

Introduction of the BAR Theorem framework for LLM service design.

Abstract

When designing LLM services, practitioners care about three key properties: inference-time budget, factual authenticity, and reasoning capacity. However, our analysis shows that no model can simultaneously optimize for all three. We formally prove this trade-off and propose a principled framework named The BAR Theorem for LLM-application design.