Transformer-based large language models (LLMs) typically have a limited context window, resulting in significant performance degradation when processing text beyond the length of the context window. Extensive studies have been proposed to extend the context window and achieve length extrapolation of LLMs, but there is still a lack of in-depth interpretation of these approaches. In this study, we explore the positional information within and beyond the context window for deciphering the underlying mechanism of LLMs. By using a mean-based decomposition method, we disentangle positional vectors from hidden states of LLMs and analyze their formation and effect on attention. Furthermore, when texts exceed the context window, we analyze the change of positional vectors in two settings, i.e., direct extrapolation and context window extension. Based on our findings, we design two training-free context window extension methods, positional vector replacement and attention window extension. Experimental results show that our methods can effectively extend the context window length.

Position embedding is a core component of current Large Language Models (LLMs). Rotary position embedding (RoPE), a technique that encodes the position information with a rotation matrix, has been the de facto choice for position embedding in many LLMs, such as the Llama series. RoPE has been further utilized to extend long context capability, which is roughly based on adjusting the \textit{base} parameter of RoPE to mitigate out-of-distribution (OOD) problems in position embedding. However, in this paper, we find that LLMs may obtain a superficial long-context ability based on the OOD theory. We revisit the role of RoPE in LLMs and propose a novel property of long-term decay, we derive that the \textit{base of RoPE bounds context length}: there is an absolute lower bound for the base value to obtain certain context length capability. Our work reveals the relationship between context length and RoPE base both theoretically and empirically, which may shed light on future long context training.