# GeoLatent: Geometry-Guided Latent Structuring with Routed Optimization for 3D Reasoning

arXiv: https://arxiv.org/abs/2610.02091 · HTML: https://mlsanity.com/paper/2610.02091/

## 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 36 of its 40 references that are in the map.
- First posted on arXiv 1 Oct 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 36)

- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [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)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [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)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [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)
- [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)
- [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)
- [Molmo2: Open Weights and Data for Vision-Language Models with Video Understanding and Grounding](https://mlsanity.com/paper/2601.10611/) (2026)
- [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)
- [ViewSpatial-Bench: Evaluating Multi-perspective Spatial Localization in Vision-Language Models](https://mlsanity.com/paper/2505.21500/) (2025)
- [Latent Visual Reasoning](https://mlsanity.com/paper/2509.24251/) (2025)
- [SpatialLadder: Progressive Training for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.08531/) (2025)
- [Perception Tokens Enhance Visual Reasoning in Multimodal Language Models](https://mlsanity.com/paper/2412.03548/) (2024)
- [Think with 3D: Geometric Imagination Grounded Spatial Reasoning from Limited Views](https://mlsanity.com/paper/2510.18632/) (2025)

## Abstract (arXiv)

Despite progress in vision-language models, 3D spatial reasoning from 2D images remains challenging. Text-based methods describe intermediate geometry with discrete tokens, limiting fidelity for continuous spatial relations. Continuous latents offer richer representations, but a single latent type does not explicitly separate the cues needed across spatial tasks. Decomposed spatial latents address this by representing position, direction, and global geometry separately under geometric supervision. Yet the geometry representation can still collapse toward one dominant direction, and unrestricted attention can leave the latents underused during answer learning. We introduce GeoLatent, combining Common--Residual Geometry Alignment (CR-GEO) with routed optimization to structure the geometry states while promoting latent-mediated answer learning. CR-GEO separates shared from residual teacher geometry; routed optimization jointly trains geometry and language, temporarily directs visual answer learning through the latents, and restores full attention with geometry supervision. In controlled comparisons, CR-GEO raises geometry effective rank from 1.00 to 3.87, while blocking latent readout at the bottleneck lowers direction accuracy from 89.1% to 25.8% on 128 fixed questions. After recovery, the differentiated geometry representation and latent-mediated visual route remain available alongside direct image access. GeoLatent achieves 73.0% on SPAR-Bench and 72.1% on SPBench, outperforming previously reported methods on both.