# GeoAnchor: Collaborative Reasoning via Latent Decomposition for 3D Spatial Understanding

arXiv: https://arxiv.org/abs/2607.13454 · HTML: https://mlsanity.com/paper/2607.13454/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 57 of its 65 references that are in the map.
- First posted on arXiv 15 Jul 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 57)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenes](https://mlsanity.com/paper/2308.11417/) (2023)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [GLM-4.5V and GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learning](https://mlsanity.com/paper/2507.01006/) (2025)
- [Kimi-VL Technical Report](https://mlsanity.com/paper/2504.07491/) (2025)
- [SpatialRGPT: Grounded Spatial Reasoning in Vision Language Models](https://mlsanity.com/paper/2406.01584/) (2024)
- [Structured3D: A Large Photo-realistic Dataset for Structured 3D Modeling](https://mlsanity.com/paper/1908.00222/) (2019)
- [LLaVA-OneVision-1.5: Fully Open Framework for Democratized Multimodal Training](https://mlsanity.com/paper/2509.23661/) (2025)
- [EMMA: End-to-End Multimodal Model for Autonomous Driving](https://mlsanity.com/paper/2410.23262/) (2024)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Spatial-MLLM: Boosting MLLM Capabilities in Visual-based Spatial Intelligence](https://mlsanity.com/paper/2505.23747/) (2025)
- [MiniCPM-V 4.5: Cooking Efficient MLLMs via Architecture, Data, and Training Recipe](https://mlsanity.com/paper/2509.18154/) (2025)
- [OpenDriveVLA: Towards End-to-end Autonomous Driving with Large Vision Language Action Model](https://mlsanity.com/paper/2503.23463/) (2025)
- [VLM-3R: Vision-Language Models Augmented with Instruction-Aligned 3D Reconstruction](https://mlsanity.com/paper/2505.20279/) (2025)
- [SpaceR: Reinforcing MLLMs in Video Spatial Reasoning](https://mlsanity.com/paper/2504.01805/) (2025)
- [Molmo2: Open Weights and Data for Vision-Language Models with Video Understanding and Grounding](https://mlsanity.com/paper/2601.10611/) (2026)
- [Video-3D LLM: Learning Position-Aware Video Representation for 3D Scene Understanding](https://mlsanity.com/paper/2412.00493/) (2024)
- [From Flatland to Space: Teaching Vision-Language Models to Perceive and Reason in 3D](https://mlsanity.com/paper/2503.22976/) (2025)
- [Reinforcing Spatial Reasoning in Vision-Language Models with Interwoven Thinking and Visual Drawing](https://mlsanity.com/paper/2506.09965/) (2025)
- [Machine Mental Imagery: Empower Multimodal Reasoning with Latent Visual Tokens](https://mlsanity.com/paper/2506.17218/) (2025)

## Built on by (most cited first, 1 of 1)

- [GeoLatent: Geometry-Guided Latent Structuring with Routed Optimization for 3D Reasoning](https://mlsanity.com/paper/2610.02091/) (2026)

## Abstract (arXiv)

Although multimodal large language models (MLLMs) have achieved remarkable progress, understanding 3D spatial relationships from 2D images remains a critical challenge. Existing methods primarily rely on symbolic text tokens, which inherently lack the fidelity to represent continuous geometric information. While recent methods use latent representations to enhance reasoning, relying on a single latent type cannot adapt to the diversity of spatial tasks, leading to misalignment in complex geometric scenarios. To address these limitations, we propose GeoAnchor, an interleaved text-latent reasoning framework. GeoAnchor decomposes 3D spatial information into three complementary components: position latents for object grounding, direction latents for relational orientation, and geometry latents for scene structure. These components are recombined in a structured space to construct local evidence while capturing global context, enabling dynamic and interpretable reasoning. Furthermore, we introduce a collaborative training strategy that guides the model from local spatial perception to comprehensive 3D understanding. Extensive experiments on diverse and complex 3D reasoning tasks demonstrate that GeoAnchor outperforms the state of the art, validating its effectiveness and generalization capabilities.