What Rotary Position Embedding Can Tell Us: Identifying Query and Key Weights Corresponding to Basic Syntactic or High-level Semantic Information

Transformer-based large language models (LLMs) have successfully handled various tasks. As one fundamental module in Transformers, position encoding encodes the positional information of tokens in a sequence. Specifically, rotary position embedding (RoPE), one of the most widely used techniques, encodes the positional information by dividing the query or key value with $d$ elements into $d/2$ pairs and rotating the 2d vectors corresponding to each pair of elements. Therefore, the direction of each pair and the position-related rotation jointly determine the attention score. In this paper, we show that the direction of the 2d pair is largely affected by the angle between the corresponding weight vector pair. We theoretically show that non-orthogonal weight vector pairs lead to great attention on tokens at a certain relative position and are less sensitive to the input which may correspond to basic syntactic information. Meanwhile, the orthogonal weight vector pairs are more flexible regarding the relative position, which may correspond to high-level syntactic information. Empirical evidence supports the hypothesis that shallow layers of LLMs focus more on local syntax and deep layers focus more on high-level semantics. Furthermore, we show that LLMs fine-tuning mainly changes the pairs of weight vectors that are nearly orthogonal, i.e., the weight corresponding to high-level semantics, which enables the reduction of the number of trainable parameters during fine-tuning without sacrificing performance. We propose a method namely Angle-based Weight Selection (AWS) to reduce the fine-tuning overhead and verify the effectiveness of the proposed method on widely used Alpaca fine-tuned Llama-2.