Liu

Operads proposed as mathematical foundation for LLM question decomposition and consistency

Researchers propose operads — algebraic structures modeling many-in, one-out compositions — as a rigorous mathematical framework for question decomposition in LLMs. They define a 'questions operad' where QA models are interpreted as algebras, and introduce 'operadic consistency' as a measure of whether a model's answers agree across partial collapses of a decomposition tree. A companion empirical paper reports operadic consistency is strongly correlated with accuracy across twelve LLMs and four multi-hop QA datasets, outperforming temperature-based self-consistency baselines. The work attempts to give formal grounding to a widely-used but theoretically underspecified reasoning strategy.