Teaching LLMs to Ask: Self-Querying Category-Theoretic Planning for Under-Specified Reasoning

2026-01-27

AI Summary

This work addresses the tendency of large language models to generate hallucinations or violate hard constraints in partially observable environments due to missing critical preconditions. To mitigate this, the authors propose Self-Querying Bidirectional Categorical Planning (SQ-BCP), which explicitly models precondition states as satisfied, violated, or unknown. By integrating self-querying with bridging assumptions to fill informational gaps and—novelty—leveraging pullback constructions from category theory to verify compatibility between plans and goals, SQ-BCP combines bidirectional search, distance-based scoring for pruning, and precondition state classification. Evaluated on WikiHow and RecipeNLG benchmarks, the method significantly reduces resource violation rates to 14.9% and 5.8%, respectively, outperforming existing baselines while preserving output quality.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Planning, Routing, and Scheduling: Planning with Language Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Inference-time planning with large language models frequently breaks under partial observability: when task-critical preconditions are not specified at query time, models tend to hallucinate missing facts or produce plans that violate hard constraints. We introduce \textbf{Self-Querying Bidirectional Categorical Planning (SQ-BCP)}, which explicitly represents precondition status (\texttt{Sat}/\texttt{Viol}/\texttt{Unk}) and resolves unknowns via (i) targeted self-queries to an oracle/user or (ii) \emph{bridging} hypotheses that establish the missing condition through an additional action. SQ-BCP performs bidirectional search and invokes a pullback-based verifier as a categorical certificate of goal compatibility, while using distance-based scores only for ranking and pruning. We prove that when the verifier succeeds and hard constraints pass deterministic checks, accepted plans are compatible with goal requirements; under bounded branching and finite resolution depth, SQ-BCP finds an accepting plan when one exists. Across WikiHow and RecipeNLG tasks with withheld preconditions, SQ-BCP reduces resource-violation rates to \textbf{14.9\%} and \textbf{5.8\%} (vs.\ \textbf{26.0\%} and \textbf{15.7\%} for the best baseline), while maintaining competitive reference quality.

Problem

• partial observability
• under-specified reasoning
• hard constraints
• precondition uncertainty
• inference-time planning

Innovation

• Self-Querying
• Categorical Planning
• Pullback Verification
• Bidirectional Search
• Under-Specified Reasoning