# The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning

arXiv: https://arxiv.org/abs/2606.11918 · HTML: https://mlsanity.com/paper/2606.11918/

## 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 18 of its 39 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [SpatialReasoner: Towards Explicit and Generalizable 3D Spatial Reasoning](https://mlsanity.com/paper/2504.20024/) (2025)
- [How Far are VLMs from Visual Spatial Intelligence? A Benchmark-Driven Perspective](https://mlsanity.com/paper/2509.18905/) (2025)
- [Mind the Gap: Benchmarking Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2503.19707/) (2025)
- [Holistic Evaluation of Multimodal LLMs on Spatial Intelligence](https://mlsanity.com/paper/2508.13142/) (2025)
- [Visual Jigsaw Post-Training Improves MLLMs](https://mlsanity.com/paper/2509.25190/) (2025)
- [SpaCE-10: A Comprehensive Benchmark for Multimodal Large Language Models in Compositional Spatial Intelligence](https://mlsanity.com/paper/2506.07966/) (2025)
- [Co-rewarding: Stable Self-supervised RL for Eliciting Reasoning in Large Language Models](https://mlsanity.com/paper/2508.00410/) (2025)
- [Reshaping Reasoning in LLMs: A Theoretical Analysis of RL Training Dynamics through Pattern Selection](https://mlsanity.com/paper/2506.04695/) (2025)
- [SSL4RL: Revisiting Self-supervised Learning as Intrinsic Reward for Visual-Language Reasoning](https://mlsanity.com/paper/2510.16416/) (2025)
- [MARBLE: A Hard Benchmark for Multimodal Spatial Reasoning and Planning](https://mlsanity.com/paper/2506.22992/) (2025)
- [Scaling Spatial Reasoning in MLLMs through Programmatic Data Synthesis](https://mlsanity.com/paper/2512.16237/) (2025)

## Abstract (arXiv)

Current Large Reasoning Models (LRMs) exhibit remarkable general capabilities but significantly underperform in spatial reasoning tasks. Existing approaches treat this gap as a knowledge deficit, relying on supervised fine-tuning (SFT) to ingest labeled spatial data from external vision sources or synthetic engines. In contrast, we argue that for many tasks, spatial reasoning capabilities are already present in pre-trained LRMs but require alignment through logical coherence under geometric 2D and 3D constraints. In this work, we propose a self-supervised reinforcement learning (RL) framework that targets the internal reasoning process without requiring ground-truth annotations. By formalizing the notion of consistency verifiers -- reward functions that check for geometric and semantic consistency under transformations -- we demonstrate that models can improve their spatial reasoning abilities. We use both image transformations, like flipping, and textual transformations, like swapping the order of objects in the question, and propose a new optimal transport-based RL strategy, OT-GRPO, which is a minimal-matching variant of group relative policy optimization tailored to pairwise verifiers. We show that this label-free consistency training approaches the accuracy of models trained with ground-truth supervision and achieves similar generalization across diverse tasks and data domains.