  In an effort to reduce the computational load of Transformers, research on
linear attention has gained significant momentum. However, the improvement
strategies for attention mechanisms typically necessitate extensive retraining,
which is impractical for large language models with a vast array of parameters.
In this paper, we present DiJiang, a novel Frequency Domain Kernelization
approach that enables the transformation of a pre-trained vanilla Transformer
into a linear complexity model with little training costs. By employing a
weighted Quasi-Monte Carlo method for sampling, the proposed approach
theoretically offers superior approximation efficiency. To further reduce the
training computational complexity, our kernelization is based on Discrete
Cosine Transform (DCT) operations. Extensive experiments demonstrate that the
proposed method achieves comparable performance to the original Transformer,
but with significantly reduced training costs and much faster inference speeds.
Our DiJiang-7B achieves comparable performance with LLaMA2-7B on various
benchmark while requires only about 1/50 training cost. Code is available at
https://github.com/YuchuanTian/DiJiang.
