Abstract: One limitation of existing Transformer-based models is that they cannot handle very long sequences as input since their self-attention operations exhibit quadratic time and space complexity. This problem becomes especially acute when Transformers are deployed on hardware platforms equipped only with CPUs. To address this issue, we propose a novel method for accelerating self-attention at inference time that works with pretrained Transformer models out-of-the-box without requiring retraining. We experiment using our method to accelerate various long-sequence Transformers, including a leading LLaMA 2-based LLM, on various benchmarks and demonstrate a greater speedup of $2.73\times$ - $7.63\times$ while retaining $98.6$% - $99.6$% of the accuracy of the original pretrained models. The code is available on our project website at https://yuzhenmao.github.io/IceFormer/.