# Thinking with Geometry: Active Geometry Integration for Spatial Reasoning arXiv: https://arxiv.org/abs/2602.06037 · HTML: https://mlsanity.com/paper/2602.06037/ ## Key facts - Cited by 18 papers in the map (data through 14 Oct 2026). - Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. - Builds on 41 of its 62 references that are in the map. - First posted on arXiv 5 Feb 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/) ## Builds on (most cited first, 30 of 41) - [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023) - [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025) - [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025) - [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024) - [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024) - [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024) - [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023) - [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025) - [Emerging Properties in Unified Multimodal Pretraining](https://mlsanity.com/paper/2505.14683/) (2025) - [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023) - [LLaVA-Video: Video Instruction Tuning With Synthetic Data](https://mlsanity.com/paper/2410.02713/) (2024) - [Seed1.5-VL Technical Report](https://mlsanity.com/paper/2505.07062/) (2025) - [π3: Permutation-Equivariant Visual Geometry Learning](https://mlsanity.com/paper/2507.13347/) (2025) - [NaVid: Video-based VLM Plans the Next Step for Vision-and-Language Navigation](https://mlsanity.com/paper/2402.15852/) (2024) - [Spatial-MLLM: Boosting MLLM Capabilities in Visual-based Spatial Intelligence](https://mlsanity.com/paper/2505.23747/) (2025) - [ReCogDrive: A Reinforced Cognitive Framework for End-to-End Autonomous Driving](https://mlsanity.com/paper/2506.08052/) (2025) - [MMSI-Bench: A Benchmark for Multi-Image Spatial Intelligence](https://mlsanity.com/paper/2505.23764/) (2025) - [VLM-3R: Vision-Language Models Augmented with Instruction-Aligned 3D Reconstruction](https://mlsanity.com/paper/2505.20279/) (2025) - [From Flatland to Space: Teaching Vision-Language Models to Perceive and Reason in 3D](https://mlsanity.com/paper/2503.22976/) (2025) - [Spatial Forcing: Implicit Spatial Representation Alignment for Vision-language-action Model](https://mlsanity.com/paper/2510.12276/) (2025) - [Cambrian-S: Towards Spatial Supersensing in Video](https://mlsanity.com/paper/2511.04670/) (2025) - [RoboRefer: Towards Spatial Referring with Reasoning in Vision-Language Models for Robotics](https://mlsanity.com/paper/2506.04308/) (2025) - [Learning from Videos for 3D World: Enhancing MLLMs with 3D Vision Geometry Priors](https://mlsanity.com/paper/2505.24625/) (2025) - [ViewSpatial-Bench: Evaluating Multi-perspective Spatial Localization in Vision-Language Models](https://mlsanity.com/paper/2505.21500/) (2025) - [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025) - [SpatialLadder: Progressive Training for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.08531/) (2025) - [Visual Spatial Tuning](https://mlsanity.com/paper/2511.05491/) (2025) - [Scaling Spatial Intelligence with Multimodal Foundation Models](https://mlsanity.com/paper/2511.13719/) (2025) - [Think with 3D: Geometric Imagination Grounded Spatial Reasoning from Limited Views](https://mlsanity.com/paper/2510.18632/) (2025) - [Ross3D: Reconstructive Visual Instruction Tuning with 3D-Awareness](https://mlsanity.com/paper/2504.01901/) (2025) ## Built on by (most cited first, 18 of 18) - [From Pixels to Words -- Towards Native One-Vision Models at Scale](https://mlsanity.com/paper/2605.28820/) (2026) - [Cambrian-P: Pose-Grounded Video Understanding](https://mlsanity.com/paper/2605.22819/) (2026) - [ProSR: Process-Shaped Spatial Reasoning for Reliable Chain-of-Thought in VLMs](https://mlsanity.com/paper/2605.25524/) (2026) - [Q-GeoMem: Question-Guided Geometric Memory for Video Spatial Reasoning](https://mlsanity.com/paper/2605.27318/) (2026) - [Learning Geometric Representations from Videos for Spatial Intelligent Multimodal Large Language Models](https://mlsanity.com/paper/2606.05833/) (2026) - [ConsiSpace: Learning Geometric Consistency Matters for Video Spatial Reasoning](https://mlsanity.com/paper/2607.17599/) (2026) - [ViSTR-Bench: Can MLLMs Reason from Continuous Visual Cues in Dynamic Scenes?](https://mlsanity.com/paper/2607.20868/) (2026) - [SpatialImaginer: Towards Adaptive Visual Imagination for Spatial Reasoning](https://mlsanity.com/paper/2604.17385/) (2026) - [GeoWeaver: Grounding Visual Tokens with Geometric Evidence before Scene Reasoning](https://mlsanity.com/paper/2605.22558/) (2026) - [Beyond Single Expert: Harmonizing Diverse Visual Priors in MLLMs for Spatial Understanding](https://mlsanity.com/paper/2607.15054/) (2026) - [Chain of Spatial Thoughts: Modality-Agnostic Spatial Grounding for Vision Language Models](https://mlsanity.com/paper/2608.10278/) (2026) - [SpatialSpeak: QA-Native Reconstruction with Local and Global Context for Spatial Chain-of-Thought Reasoning](https://mlsanity.com/paper/2609.33616/) (2026) - [SpatialSkill: Self-Evolving Skills for Cross-View Spatial Reasoning](https://mlsanity.com/paper/2609.34124/) (2026) - [Render to Reason: Novel-View Semantic Prediction Improves Spatial Understanding in VLMs](https://mlsanity.com/paper/2610.05417/) (2026) - [Explicit Geometric Chain-of-Thought for Vision-Language-Action in Autonomous Driving](https://mlsanity.com/paper/2610.10390/) (2026) - [SpatialASM: Internalizing Active Mentalization for Spatial Reasoning](https://mlsanity.com/paper/2610.13832/) (2026) - [GeoThinker-F: Endogenous Predictive World Representations for Fast Spatial Intelligence](https://mlsanity.com/paper/2610.20592/) (2026) - [DynThinker: Unifying Static 3D and Dynamic 4D Spatial Reasoning](https://mlsanity.com/paper/2610.20598/) (2026) ## Abstract (arXiv) Recent progress in spatial reasoning with Multimodal Large Language Models (MLLMs) increasingly leverages geometric priors from 3D encoders. However, most existing integration strategies remain passive: geometry is exposed as a global stream and fused in an indiscriminate manner, which often induces semantic-geometry misalignment and redundant signals. We propose GeoThinker, a framework that shifts the paradigm from passive fusion to active perception. Instead of feature mixing, GeoThinker enables the model to selectively retrieve geometric evidence conditioned on its internal reasoning demands. GeoThinker achieves this through Spatial-Grounded Fusion applied at carefully selected VLM layers, where semantic visual priors selectively query and integrate task-relevant geometry via frame-strict cross-attention, further calibrated by Importance Gating that biases per-frame attention toward task-relevant structures. Comprehensive evaluation results show that GeoThinker sets a new state-of-the-art in spatial intelligence, achieving a peak score of 72.6 on the VSI-Bench. Furthermore, GeoThinker demonstrates robust generalization and significantly improved spatial perception across complex downstream scenarios, including embodied referring and autonomous driving. Our results indicate that the ability to actively integrate spatial structures is essential for next-generation spatial intelligence. Code can be found at https://github.com/Li-Hao-yuan/GeoThinker.