ComRoPE: Scalable and Robust Rotary Position Embedding Parameterized by Trainable Commuting Angle Matrices

TL;DR

ComRoPE introduces trainable commuting angle matrices to enhance rotary positional encoding in Transformers, improving scalability, robustness, and performance over existing methods, with theoretical analysis and state-of-the-art results on ImageNet-1K.

Contribution

It generalizes RoPE using trainable commuting angle matrices, providing a scalable, robust, and theoretically grounded positional encoding method with superior performance.

Findings

Surpasses state-of-the-art by 1.6% at training resolution.

Achieves 2.9% higher accuracy at higher resolution.

Theoretically ensures consistent performance with position offsets.

Abstract

The Transformer architecture has revolutionized various regions since it was proposed, and its effectiveness largely depends on the ability to encode positional information. Traditional position encoding methods exhibit significant limitations due to lack of robustness and flexibility of position. Therefore, Rotary Positional Encoding (RoPE) was proposed to alleviate these issues, which integrates positional information by rotating the embeddings in the attention mechanism. However, RoPE requires manually defined rotation matrices with limited transformation space, constraining the model's capacity. In this work, we propose ComRoPE, which generalizes RoPE by defining it in terms of trainable commuting angle matrices. Specifically, we demonstrate that pairwise commutativity of these matrices is essential for RoPE to achieve scalability and positional robustness. We formally define the RoPE Equation, which is an essential condition that ensures consistent performance with position offsets. Based on the theoretical analysis, we present two types of trainable commuting angle matrices as sufficient solutions to the RoPE equation, which significantly improve performance, surpassing the current state-of-the-art method by 1.6% at training resolution and 2.9% at higher resolution on the ImageNet-1K dataset. Furthermore, our framework shows versatility in generalizing to existing RoPE formulations and offering new insights for future positional encoding research. To ensure reproducibility, the source code and instructions are available at https://github.com/Longin-Yu/ComRoPE