Solving Attention Kernel Regression Problem via Pre-conditioner

Large language models have shown impressive performance in many tasks. One of the major features from the computation perspective is computing the attention matrix. Previous works [Zandieh, Han, Daliri, and Karba 2023, Alman and Song 2023] have formally studied the possibility and impossibility of approximating the attention matrix. In this work, we define and study a new problem which is called the attention kernel regression problem. We show how to solve the attention kernel regression in the input sparsity time of the data matrix.