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Self-attention and position embedding are two key modules in Transformerbased LLMs. The potential relationship among them are far from well studied,especially for context window extending. In this paper, we introduce collinearconstrained relationship to fuse RoPE and self-attention, and name it asCollinear Constrained Attention (CoCA). We've analyzed the computational andspatial complexity of CoCA and have determined that it adds only minimaladditional overhead compared to the original Transformer-based models. Weprovide an efficient implementation of CoCA, and make it drop-in replacementfor any existing position embedding and attention modules in Transformer basedmodels. Experiments show that CoCA performs extraordinary well on contextwindow extending. For instance, a CoCA based GPT model trained with 512 contextlength can extend the context window up to 8K without perplexity diverging.This indicates more than 16x context window extending without any fine-tuning.Our code is released here:https://github.com/codefuse-ai/Collinear-Constrained-Attention

CoCA: Fusing position embedding with Collinear Constrained Attention for fine-tuning free context window extending