TIGeR: Tool-Integrated Geometric Reasoning in Vision-Language Models for Robotics

TL;DR

TIGeR reframes vision-language models as geometric computers by enabling external, tool-based computations on calibrated metric data to achieve centimeter-level precision in robotics. It introduces TIGeR-300K, a large dataset of tool-invocation–oriented geometric reasoning samples, and a two-stage SFT-RFT training pipeline with hierarchical rewards to train precise geometric computation and robust tool usage. The framework categorizes tools into perception and geometric computation, integrates a code-generation subroutine, and demonstrates state-of-the-art geometric reasoning on benchmarks, simulations, and real-robot tasks. By offloading exact computations to external tools, TIGeR provides interpretable, adaptable, and scalable geometric reasoning for embodied robotics without requiring end-to-end neural precision in all geometric operations.

Abstract

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.

Figures (6)

• Figure 1: TIGeR is a tool-integrated framework that enables exact geometric reasoning and computation via code generation and execution on calibrated metric inputs. It can achieve accurate spatial localization, unified reasoning across viewpoints, and address complex embodied tasks requiring accurate numerical computation, with high interpretability and adaptability.
• Figure 2: TIGeR-300K: A VQA dataset comprising 300K samples with Tool-Integrated Geometric Reasoning, generated via template-based synthesis and tool-augmentation by LLMs. It contains problem statements and solutions with a complete tool invocation sequence and intermediate computations tailored for our proposed hierarchical reward design.
• Figure 3: TIGeR's two-stage training pipeline. The process begins with SFT on TIGeR-300K, followed by RFT incorporating five specialized reward functions (outcome- and process-based) tailored for TIR to enhance geometric reasoning abilities.
• Figure 4: Comparison between TIGeR and Gemini 2.5-Pro on representative samples from spatial understanding benchmarks.
• Figure 5: Illustration of TIGeR’s tool-integrated reasoning in real-robot tasks.. "Pick up the drumstick and place it to the back of the brown toy" requires precise 3D spatial reasoning to localize the target position despite occlusion of the rear region. Similarly, "Place the black bag in an empty area on the table" demands complex geometric computation to identify feasible free space in cluttered scenes. We visualize the robot’s execution through sequential video frames, along with TIGeR’s step-by-step tool calls and their outputs, overlaid on the corresponding images.