# GIFT: Geometry-Induced Functional Transfer for Category-level Object Manipulation

arXiv: https://arxiv.org/abs/2503.15371 · HTML: https://mlsanity.com/paper/2503.15371/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Imitation from Observation: Learning to Imitate Behaviors from Raw Video via Context Translation](https://mlsanity.com/paper/1707.03374/) (2017)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [Learning Robotic Manipulation Policies from Point Clouds with Conditional Flow Matching](https://mlsanity.com/paper/2409.07343/) (2024)
- [SE(3)-Equivariant Relational Rearrangement with Neural Descriptor Fields](https://mlsanity.com/paper/2211.09786/) (2022)
- [AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies](https://mlsanity.com/paper/2402.04292/) (2024)
- [CaTGrasp: Learning Category-Level Task-Relevant Grasping in Clutter from Simulation](https://mlsanity.com/paper/2109.09163/) (2021)
- [DINOBot: Robot Manipulation via Retrieval and Alignment with Vision Foundation Models](https://mlsanity.com/paper/2402.13181/) (2024)
- [kPAM 2.0: Feedback Control for Category-Level Robotic Manipulation](https://mlsanity.com/paper/2102.06279/) (2021)
- [Learning One-Shot Imitation from Humans without Humans](https://mlsanity.com/paper/1911.01103/) (2019)
- [Imitation Learning from Video by Leveraging Proprioception](https://mlsanity.com/paper/1905.09335/) (2019)
- [Motion Reasoning for Goal-Based Imitation Learning](https://mlsanity.com/paper/1911.05864/) (2019)
- [DQ Robotics: a Library for Robot Modeling and Control](https://mlsanity.com/paper/1910.11612/) (2019)
- [SpectGRASP: Robotic Grasping by Spectral Correlation](https://mlsanity.com/paper/2107.12492/) (2021)
- [Grasp Transfer for Deformable Objects by Functional Map Correspondence](https://mlsanity.com/paper/2203.00776/) (2022)
- [Grasp Transfer based on Self-Aligning Implicit Representations of Local Surfaces](https://mlsanity.com/paper/2308.07807/) (2023)
- [Coordinate Invariant User-Guided Constrained Path Planning with Reactive Rapidly Expanding Plane-Oriented Escaping Trees](https://mlsanity.com/paper/2203.10649/) (2022)

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

- [In-Context Learning for Robots: Methods and Applications](https://mlsanity.com/paper/2609.36012/) (2026)

## Abstract (arXiv)

Robotic manipulation of unfamiliar objects in new environments is challenging due to limited generalisation capabilities. We propose a new skill transfer framework, GIFT (Geometry-Induced Functional Transfer), which enables a robot to transfer complex object manipulation skills and constraints from a single human demonstration. Our approach addresses the challenge of skill acquisition and task execution by deriving geometric representations from demonstrations focusing on object-centric interactions. By leveraging the Functional Maps (FMC) framework, we efficiently map interaction functions between objects and their environments, allowing the robot to replicate task operations across objects of similar topologies or categories, even when they have significantly different shapes. Additionally, our method incorporates screw interpolation (ScLERP) for generating smooth, geometrically-aware robot paths to ensure the transferred skills adhere to the demonstrated task constraints. We validate the effectiveness and adaptability of our approach through extensive experiments, demonstrating successful skill transfer and task execution in diverse real-world environments without requiring additional training.