Research map / Large language models / Reasoning and chain of thought

Operads for compositional reasoning in LLMs

NeurIPS 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 0 citations (OpenAlex)

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Proposes modeling LLM question decomposition with operads, defining a questions operad and an operadic consistency diagnostic, with empirical evaluation deferred to a companion paper.

Problem

Question decomposition, used to improve LLM reasoning, lacks a rigorous mathematical foundation, and there is no principled way to define correctness or error propagation for decompositions without ground-truth labels.

Approach

Model question decomposition as the questions operad, in which operations are question templates with blanks and composition is substitution of sub-answers; interpret QA models as algebras over it and define operadic consistency as agreement of answers across partial collapses of a question decomposition tree.

Key results

• Illustrative example: Llama 3 8B Instruct gives three different answers ('Bess Truman' x3 vs 'Eleanor Roosevelt') across four partial collapses of one tree of questions, witnessing operadic inconsistency.
• Companion paper (not in this text) reportedly finds operadic consistency strongly correlated with accuracy across twelve LLMs and four multi-hop QA datasets, outperforming temperature-based self-consistency.

Limitations

• No empirical evaluation in this paper; results are deferred to a companion paper.
• Associativity holds only up to semantic equivalence when questions are realized in natural language.
• Depth-2 chain extraction is a minimal first attempt at formalizing reasoning traces.

Experimental setup

Builds on: chain-of-thought prompting decomposed prompting uncertainty of thoughts May's operad theory

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