# TIGeR: Tool-Integrated Geometric Reasoning in Vision-Language Models for Robotics arXiv: https://arxiv.org/abs/2510.07181 ยท HTML: https://mlsanity.com/paper/2510.07181/ ## Key facts - Cited by 27 papers in the map (data through 14 Oct 2026). - Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. - Builds on 74 of its 88 references that are in the map. - First posted on arXiv 8 Oct 2025. ## 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 74) - [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023) - [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) - [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025) - [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023) - [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024) - [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025) - [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025) - [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022) - [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (2022) - [Cambrian-1: A Fully Open, Vision-Centric Exploration of Multimodal LLMs](https://mlsanity.com/paper/2406.16860/) (2024) - [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024) - [BLINK: Multimodal Large Language Models Can See but Not Perceive](https://mlsanity.com/paper/2404.12390/) (2024) - [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025) - [Florence-2: Advancing a Unified Representation for a Variety of Vision Tasks](https://mlsanity.com/paper/2311.06242/) (2023) - [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025) - [R1-Searcher: Incentivizing the Search Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.05592/) (2025) - [WebThinker: Empowering Large Reasoning Models with Deep Research Capability](https://mlsanity.com/paper/2504.21776/) (2025) - [SpatialRGPT: Grounded Spatial Reasoning in Vision Language Models](https://mlsanity.com/paper/2406.01584/) (2024) - [Recognize Anything: A Strong Image Tagging Model](https://mlsanity.com/paper/2306.03514/) (2023) - [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023) - [MoGe-2: Accurate Monocular Geometry with Metric Scale and Sharp Details](https://mlsanity.com/paper/2507.02546/) (2025) - [RoboPoint: A Vision-Language Model for Spatial Affordance Prediction for Robotics](https://mlsanity.com/paper/2406.10721/) (2024) - [Spatial-MLLM: Boosting MLLM Capabilities in Visual-based Spatial Intelligence](https://mlsanity.com/paper/2505.23747/) (2025) - [NVILA: Efficient Frontier Visual Language Models](https://mlsanity.com/paper/2412.04468/) (2024) - [AnyGrasp: Robust and Efficient Grasp Perception in Spatial and Temporal Domains](https://mlsanity.com/paper/2212.08333/) (2022) - [ZeroSearch: Incentivize the Search Capability of LLMs without Searching](https://mlsanity.com/paper/2505.04588/) (2025) - [HybridVLA: Collaborative Diffusion and Autoregression in a Unified Vision-Language-Action Model](https://mlsanity.com/paper/2503.10631/) (2025) - [RoboMIND: Benchmark on Multi-embodiment Intelligence Normative Data for Robot Manipulation](https://mlsanity.com/paper/2412.13877/) (2024) - [ToRL: Scaling Tool-Integrated RL](https://mlsanity.com/paper/2503.23383/) (2025) ## Built on by (most cited first, 27 of 27) - [Zooming without Zooming: Region-to-Image Distillation for Fine-Grained Multimodal Perception](https://mlsanity.com/paper/2602.11858/) (2026) - [Geometrically-Constrained Agent for Spatial Reasoning](https://mlsanity.com/paper/2511.22659/) (2025) - [Robobench: A Comprehensive Evaluation Benchmark for Multimodal Large Language Models as Embodied Brain](https://mlsanity.com/paper/2510.17801/) (2025) - [Think3D: Thinking with Space for Spatial Reasoning](https://mlsanity.com/paper/2601.13029/) (2026) - [SpaceTools: Tool-Augmented Spatial Reasoning via Double Interactive RL](https://mlsanity.com/paper/2512.04069/) (2025) - [From Language to Locomotion: Retargeting-free Humanoid Control via Motion Latent Guidance](https://mlsanity.com/paper/2510.14952/) (2025) - [Scaling Agentic Reinforcement Learning for Tool-Integrated Reasoning in VLMs](https://mlsanity.com/paper/2511.19773/) (2025) - [SpatialClaw: Rethinking Action Interface for Agentic Spatial Reasoning](https://mlsanity.com/paper/2606.13673/) (2026) - [Towards Spatial Trace with Reasoning in Vision-Language Models for Robotics](https://mlsanity.com/paper/2512.13660/) (2025) - [SaPaVe: Towards Active Perception and Manipulation in Vision-Language-Action Models for Robotics](https://mlsanity.com/paper/2603.12193/) (2026) - [RoboStream: Weaving Spatio-Temporal Reasoning with Memory in Vision-Language Models for Robotics](https://mlsanity.com/paper/2603.12939/) (2026) - [Allocentric Perceiver: Disentangling Allocentric Reasoning from Egocentric Visual Priors via Frame Instantiation](https://mlsanity.com/paper/2602.05789/) (2026) - [Thinking with Imagination: Agentic Visual Spatial Reasoning with World Simulators](https://mlsanity.com/paper/2606.06476/) (2026) - [BOP-ASK: Object-Interaction Reasoning for Vision-Language Models](https://mlsanity.com/paper/2511.16857/) (2025) - [RieMind: Geometry-Grounded Spatial Agent for Scene Understanding](https://mlsanity.com/paper/2603.15386/) (2026) - [Self-Evolving Neuro-Symbolic Skills for Tool-Augmented Spatial Reasoning](https://mlsanity.com/paper/2608.07955/) (2026) - [LAST: Leveraging Tools as Hints to Enhance Spatial Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2604.09712/) (2026) - [AssemLM: A Spatial Reasoning Multimodal Large Language Model for Robotic Assembly](https://mlsanity.com/paper/2604.08983/) (2026) - [SATURN: Symbolic Spatial Reasoning for Multi-Perspective Grounding](https://mlsanity.com/paper/2606.22694/) (2026) - [OmniView-Space: Reinforcing Spatial Reasoning via Multi-Perspective Spatial Mapping](https://mlsanity.com/paper/2607.00881/) (2026) - [SpatialCLI: Learning to Reason With Spatial Tools, Then Without Them](https://mlsanity.com/paper/2607.27703/) (2026) - [Skill-3D: Evolving Scene-Aware Skills for Agentic 3D Spatial Reasoning](https://mlsanity.com/paper/2606.07436/) (2026) - [Diagnosing Semantic Handoff Failures in Agent-Orchestrated Vision-Language-Action Skill Composition](https://mlsanity.com/paper/2607.06256/) (2026) - [MAG-3D: Multi-Agent Grounded Reasoning for 3D Understanding](https://mlsanity.com/paper/2604.09167/) (2026) - [Disentangling 3D Modeling from Spatial Reasoning](https://mlsanity.com/paper/2608.05242/) (2026) - [ActiveArena: Benchmarking and Understanding Active Perception in Robotic Manipulation](https://mlsanity.com/paper/2609.24124/) (2026) - [Distilling Routed 3D Privilege for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2610.12355/) (2026) ## Abstract (arXiv) Vision-Language Models (VLMs) have shown remarkable capabilities in spatial reasoning, yet they remain fundamentally limited to qualitative precision and lack the computational precision required for real-world robotics. Current approaches fail to leverage metric cues from depth sensors and camera calibration, instead reducing geometric problems to pattern recognition tasks that cannot deliver the centimeter-level accuracy essential for robotic manipulation. We present TIGeR (Tool-Integrated Geometric Reasoning), a novel framework that transforms VLMs from perceptual estimators to geometric computers by enabling them to generate and execute precise geometric computations through external tools. Rather than attempting to internalize complex geometric operations within neural networks, TIGeR empowers models to recognize geometric reasoning requirements, synthesize appropriate computational code, and invoke specialized libraries for exact calculations. To support this paradigm, we introduce TIGeR-300K, a comprehensive tool-invocation-oriented dataset covering point transformations, pose estimation, and spatial compatibility verification, complete with tool invocation sequences and intermediate computations. Through a two-stage training pipeline combining supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT) with our proposed hierarchical reward design, TIGeR achieves SOTA performance on geometric reasoning benchmarks while demonstrating centimeter-level precision in real-world robotic manipulation tasks.