DoPE: Denoising Rotary Position Embedding

Positional encoding is essential for large language models (LLMs) to represent sequence order, yet recent studies show that Rotary Position Embedding (RoPE) can induce massive activation. We investigate the source of these instabilities via a spectral analysis of RoPE, and show that its low-frequency components concentrate structured energy, producing low-rank, over-aligned attention patterns. We theoretically reveal that this low-frequency alignment manifests as activation noise, degrading stability during long-context extrapolation. To mitigate this effect, we introduce Denoising Rotary Position Embedding (DoPE), a training-free method that identifies and suppresses noisy attention heads using truncated matrix entropy, then reparameterizes their attention maps with an isotropic Gaussian distribution. Across a range of settings, DoPE improves length extrapolation performance without fine-tuning, increases robustness to perturbations, and boosts both needle-in-a-haystack and many-shot in-context learning tasks. These results suggest that selective positional encoding is key to robust extrapolation. Our project page is Project: https://The-physical-picture-of-LLMs.github.io