Learning the RoPEs: Better 2D and 3D Position Encodings with STRING

Connor Schenck, Isaac Reid, Mithun George Jacob, Alex Bewley, Joshua Ainslie, David Rendleman, Deepali Jain, Mohit Sharma, Kumar Avinava Dubey, Ayzaan Wahid, Sumeet Singh, René Wagner, Tianli Ding, Chuyuan Fu, Arunkumar Byravan, Jake Varley, Alexey A. Gritsenko, Matthias Minderer, Dmitry Kalashnikov, Jonathan Tompson et al. (2 additional authors not shown)

Track: full paper

Keywords: position encodings for Transformers, RoPE, Robotics, translation-invariance, Lie algebra

TL;DR: This paper introduces STRING: a general class of separable translation-invariant position encodings for Transformers (extending Rotary Position Encodings), and applies them in a wide range of 2D and 3D scenarios, in particular in Robotics.

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 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.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Format: Yes, the presenting author will definitely attend in person because they are attending ICLR for other complementary reasons.

Funding: No, the presenting author of this submission does *not* fall under ICLR’s funding aims, or has sufficient alternate funding.

Submission Number: 76