Abstract: We introduce $\textbf{STRING}$: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides $\textbf{exact}$ translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers.We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods. Videos of STRING-based robotics controllers can be found here: https://sites.google.com/view/string-robotics.

Lay Summary:

This paper introduces STRING, a new and improved method for AI to understand the position of items, especially in 2D images and 3D scenes. Current AI models (Transformers) grasp content but struggle with order or location. STRING builds upon a popular method called RoPE but is more general and better suited for multi-dimensional data. It retains RoPE's key benefits—encoding each item's position independently ("separability") and focusing on relative distances ("translational invariance")—while being more powerful. The paper proves STRING is theoretically the most comprehensive approach of its kind under certain conditions. Crucially, it delivers significant performance gains in practical applications like object detection and robotics control, where efficiently representing 2D/3D information is vital. In short, STRING helps AI "see" and understand spatial arrangements more effectively.