# Self-Evolving Spatial Reasoning in Vision Language Models via Geometric Logic Consistency

arXiv: https://arxiv.org/abs/2605.18162 · HTML: https://mlsanity.com/paper/2605.18162/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 66 references that are in the map.
- First posted on arXiv 18 May 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)
- Synthetic data and self-improvement for LLMs / [Self-improving MLLMs and synthetic data](https://mlsanity.com/synth/self-improving-mllms-and-synthetic-data/)

## Builds on (most cited first, 14 of 14)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Video-MMMU: Evaluating Knowledge Acquisition from Multi-Discipline Professional Videos](https://mlsanity.com/paper/2501.13826/) (2025)
- [SpaceR: Reinforcing MLLMs in Video Spatial Reasoning](https://mlsanity.com/paper/2504.01805/) (2025)
- [ViewSpatial-Bench: Evaluating Multi-perspective Spatial Localization in Vision-Language Models](https://mlsanity.com/paper/2505.21500/) (2025)
- [ViSS-R1: Self-Supervised Reinforcement Video Reasoning](https://mlsanity.com/paper/2511.13054/) (2025)
- [Faithful GRPO: Improving Visual Spatial Reasoning in Multimodal Language Models via Constrained Policy Optimization](https://mlsanity.com/paper/2604.08476/) (2026)
- [SpatialEvo: Self-Evolving Spatial Intelligence via Deterministic Geometric Environments](https://mlsanity.com/paper/2604.14144/) (2026)

## Built on by (most cited first, 3 of 3)

- [Spatial Memory Agent: Experience-Grounded Procedure Memory for Spatial Intelligence](https://mlsanity.com/paper/2608.12743/) (2026)
- [Symmetry-Aware Likelihood-Orbit Aggregation for Selective Left-Right Claim Verification](https://mlsanity.com/paper/2609.17004/) (2026)
- [SpatialSkill: Self-Evolving Skills for Cross-View Spatial Reasoning](https://mlsanity.com/paper/2609.34124/) (2026)

## Abstract (arXiv)

Vision-Language Models (VLMs) have made striking progress, yet their spatial reasoning remains fragile. Models that answer an original input correctly can still fail under valid transformations with predictable answer mappings, revealing a gap between instance-level correctness and robust spatial reasoning. To address this, we propose Spatial Alignment via Geometric Evolution (SAGE), a self-evolving framework that improves robust spatial reasoning through geometric and linguistic duality operations. SAGE incorporates duality consistency into GRPO training, encouraging models to produce coherent answers across original and transformed inputs. SAGE co-evolves duality generation and solution, allowing the model to continually expose and address its own reasoning weaknesses. A dynamic operation pool identifies challenging operations and retires mastered ones, keeping training focused on informative duality signals. SAGE is model-agnostic, data-efficient compared to prior post-training methods, and can be applied as a lightweight adaptation stage to any existing VLM. Experiments on video and spatial reasoning benchmarks demonstrate consistent improvements over strong baselines and enhanced generalization to unseen data.