Fast Matrix Multiplications for Lookup Table-Quantized LLMs
Authors: name: Han Guo, name: William Brandon, name: Radostin Cholakov, name: Jonathan Ragan-Kelley, name: Eric P. Xing, name: Yoon Kim

The deployment of large language models (LLMs) is often constrained by memory
bandwidth, where the primary bottleneck is the cost of transferring model
parameters from the GPU's global memory to its registers. When coupled with
custom kernels that fuse the dequantization and matmul operations, weight-only
quantization can thus enable faster inference by reducing the amount of memory
movement. However, developing high-performance kernels for weight-quantized
LLMs presents substantial challenges, especially when the weights are
compressed to non-evenly-divisible bit widths (e.g., 3 bits) with non-uniform,
lookup table (LUT) quantization. This paper describes FLUTE, a flexible lookup
table engine for LUT-quantized LLMs, which uses offline restructuring of the
quantized weight matrix to minimize bit manipulations associated with
unpacking, and vectorization and duplication of the lookup table to mitigate
shared memory bandwidth constraints. At batch sizes < 32 and quantization group
size of 128 (typical in LLM inference), the FLUTE kernel can be 2-4x faster
than existing GEMM kernels. As an application of FLUTE, we explore a simple
extension to lookup table-based NormalFloat quantization and apply it to
quantize LLaMA3 to various configurations, obtaining competitive quantization
performance against strong baselines while obtaining an end-to-end throughput
increase of 1.5 to 2 times.