SymboUQ: Symbolic Uncertainty Quantification for Spatial Reasoning in LLMs
On the map: LLM reasoning → Spatial and embodied reasoning
Abstract (arXiv)
Although large language models (LLMs) can produce fluent spatial reasoning traces, their intermediate relations may fail to support the final conclusion, making token-level confidence insufficient for final-answer reliability estimation. Existing formal verifiers provide stronger semantic evidence, but their applicability is partial: a parsed claim need not yield a definite semantic verdict. To address this issue, we introduce SymboUQ, a symbolic uncertainty quantification framework that estimates final-answer reliability from reasoning traces by distinguishing symbolizability, whether a claim can be represented in the verifier's formal language, from semantic determinacy, whether its execution yields an entailed or contradicted verdict rather than an unknown or not-evaluable outcome. SymboUQ comprises (i) a Layout Auditor that executes ordered spatial claims and extracts feasibility, conflict, and repair evidence; (ii) a label-free Determinacy Profile that characterizes effective executable coverage; and (iii) a Determinacy-Aware Reliability Composer that integrates constraint-based, representation-based, and decoding-based scores according to verifier applicability. Extensive experiments on five spatial reasoning benchmarks with four frozen LLM backbones show that SymboUQ achieves approximately an 8% relative improvement in AUROC and a 7% relative reduction in class-balanced Brier loss over the strongest baseline.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. Builds on 8 of its 31 references that are in the map. First posted on arXiv 1 Aug 2026.
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References · 8
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