# SymboUQ: Symbolic Uncertainty Quantification for Spatial Reasoning in LLMs

arXiv: https://arxiv.org/abs/2608.00417 · HTML: https://mlsanity.com/paper/2608.00417/

## 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.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 8 of 8)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [BEAVER: An Efficient Deterministic LLM Verifier](https://mlsanity.com/paper/2512.05439/) (2025)
- [Distributional Energy-Based Models for Uncertainty-Aware Structured LLM Reasoning](https://mlsanity.com/paper/2605.18871/) (2026)

## 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.