# LeRF: Learning Reference Coordinate Frames for Perspective Taking Reasoning

arXiv: https://arxiv.org/abs/2609.36219 · HTML: https://mlsanity.com/paper/2609.36219/

## 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 26 of its 32 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 26 of 26)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [GLM-4.5V and GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learning](https://mlsanity.com/paper/2507.01006/) (2025)
- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [BEDLAM: A Synthetic Dataset of Bodies Exhibiting Detailed Lifelike Animated Motion](https://mlsanity.com/paper/2306.16940/) (2023)
- [Qwen3.5-Omni Technical Report](https://mlsanity.com/paper/2604.15804/) (2026)
- [Objectron: A Large Scale Dataset of Object-Centric Videos in the Wild with Pose Annotations](https://mlsanity.com/paper/2012.09988/) (2020)
- [3DSRBench: A Comprehensive 3D Spatial Reasoning Benchmark](https://mlsanity.com/paper/2412.07825/) (2024)
- [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)
- [EmbSpatial-Bench: Benchmarking Spatial Understanding for Embodied Tasks with Large Vision-Language Models](https://mlsanity.com/paper/2406.05756/) (2024)
- [EMDB: The Electromagnetic Database of Global 3D Human Pose and Shape in the Wild](https://mlsanity.com/paper/2308.16894/) (2023)
- [VTool-R1: VLMs Learn to Think with Images via Reinforcement Learning on Multimodal Tool Use](https://mlsanity.com/paper/2505.19255/) (2025)
- [SpatialReasoner: Towards Explicit and Generalizable 3D Spatial Reasoning](https://mlsanity.com/paper/2504.20024/) (2025)
- [Do Vision-Language Models Represent Space and How? Evaluating Spatial Frame of Reference Under Ambiguities](https://mlsanity.com/paper/2410.17385/) (2024)
- [Omni6DPose: A Benchmark and Model for Universal 6D Object Pose Estimation and Tracking](https://mlsanity.com/paper/2406.04316/) (2024)
- [Perspective-Aware Reasoning in Vision-Language Models via Mental Imagery Simulation](https://mlsanity.com/paper/2504.17207/) (2025)
- [ImageNet3D: Towards General-Purpose Object-Level 3D Understanding](https://mlsanity.com/paper/2406.09613/) (2024)
- [Orient Anything V2: Unifying Orientation and Rotation Understanding](https://mlsanity.com/paper/2601.05573/) (2026)
- [OmniNOCS: A unified NOCS dataset and model for 3D lifting of 2D objects](https://mlsanity.com/paper/2407.08711/) (2024)
- [Thinking with Blueprints: Assisting Vision-Language Models in Spatial Reasoning via Structured Object Representation](https://mlsanity.com/paper/2601.01984/) (2026)
- [SpinBench: Perspective and Rotation as a Lens on Spatial Reasoning in VLMs](https://mlsanity.com/paper/2509.25390/) (2025)
- [MultihopSpatial: Multi-hop Compositional Spatial Reasoning Benchmark for Vision-Language Model](https://mlsanity.com/paper/2603.18892/) (2026)

## Abstract (arXiv)

Perspective taking is a fundamental component of spatial intelligence, requiring models interpret spatial relations from a specified viewpoint, such as that of another entity or an imagined observer. Despite the increasing spatial reasoning capabilities of Vision-Language Models (VLMs), they still struggle with perspective taking, often defaulting to the camera viewpoint when a query requires reasoning from a different perspective. We introduce Learning Reference Coordinate Frames for Perspective Taking (LeRF), a framework that trains VLMs to construct and use explicit reference frames for viewpoint-dependent reasoning. Given an image and a query, LeRF decides whether a coordinate frame is necessary. If so, it grounds the reference entity and predicts the frame's origin and entity-centered reference frame. A lightweight renderer overlays the frame onto the image, enabling subsequent reasoning over these visual cues without external perception models or explicit 3D reconstruction. To learn this process, we first perform supervised fine-tuning to teach selective tool invocation and reference coordinate frame prediction, followed by reinforcement learning on spatial VQA pairs to improve frame-guided reasoning. Across diverse perspective-taking benchmarks, LeRF consistently improves over its backbone and achieves strong performance against existing open-source methods. Further evaluations also show improved reference-frame grounding and orientation estimation, supporting the effectiveness of learned reference frames for viewpoint-dependent reasoning.