Title: Decoupling The "What" and "Where" With Polar Coordinate Positional Embedding
Primary area: foundation or frontier models, including LLMs
Keywords: relative positional encoding, RoPE, Transformers, sequence modelling, length generalization, complex-valued activations

Abstract: The attention mechanism in a Transformer architecture matches key to query based on both content---the *what*---and position in a sequence---the *where*. We present an analysis indicating that what and where are entangled in the popular rotary position embedding (RoPE). This entanglement can impair performance particularly when decisions require independent matches on these two factors. We propose an improvement to RoPE, which we call *Polar Coordinate Position Embedding* or *PoPE*, that eliminates the what-where confound. PoPE is far superior on a diagnostic task requiring indexing solely by position or by content. On autoregressive sequence modeling in music, genomic, and natural language domains, Transformers using PoPE as the positional encoding scheme outperform baselines using RoPE with respect to evaluation loss (perplexity) and downstream task performance. On language modeling, these gains persist across model scale, from 124M to 774M parameters. Crucially, PoPE shows strong zero-shot length extrapolation capabilities, whereas RoPE's performance degrades significantly on longer sequences at test time without fine tuning or the use of position-interpolation methods.

TL;DR: We propose an improvement to RoPE that decouples the matches based on content and positional information leading to improved sequence modeling performance across several domains and strong zero-shot length generalization.