Efficient inference on large language models (LLMs) has become a popular topic in both academia and industry. Roughly speaking, LLMs consist of a collection of weight matrices, and generative inference on these models essentially computes a sequence of matrix-vector products and thus can be heavily memory-bound. Consequently, much work has been devoted to reducing the size of the weights to lower bit-widths through various forms of quantization. In turn, these diverse precision formats complicate both the arithmetic and optimized kernel implementation.
So far, the vast majority of implementation work for mixed-precision LLM computation has been done manually. Currently, one of the most powerful and complex scalar LLM compression techniques is \emph{nonuniform} quantization, in which a matrix is divided unevenly into parts that are quantized with different bit-widths, minimizing the output compression error. In this paper, we present QIGen, the first kernel generator for LLM inference on CPUs to support nonuniform quantization in full generality. Given a nonuniformly quantized LLM and target CPU characteristics, QIGen first generates the diverse set of needed custom matrix-vector product kernels and combines them with a suitable storage format.
We benchmark and analyze QIGen-generated code in various experiments. In particular, we show that our code achieves Pareto optimality in terms of performance and accuracy with respect to the most used open-source tool. We show a speedup of up to $1.3\times$ for the matrix-vector and $3.4\times$ for the matrix-matrix computations even when using uniform quantization.