Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach

Abstract

As large language models scale, memory bandwidth for key-value caches and retrieval-augmented generation systems becomes a critical bottleneck. While 1-bit quantization addresses this constraint, recent TurboQuant relies on dense random rotation matrices to condition the vector distribution before quantization. This projection demands millions of floating-point multiplications per embedding, making it difficult to deploy on constrained edge silicon. We introduce Fast-TurboQuant, a multiplier-free projection architecture that replaces the dense matrix with a structured fast Johnson-Lindenstrauss transform. By applying a Rademacher phase inversion followed by a fast Walsh-Hadamard transform (FWHT), the method leverages sub-Gaussian concentration to satisfy the prerequisites of scalar Lloyd-Max quantization without Gaussian projections. This substitution reduces the arithmetic complexity to only additions, eliminating hardware multipliers. Evaluation on DBpedia OpenAI-3 Large embeddings demonstrates a 19.7 times algorithmic speedup under sequential execution. Furthermore, the dimension expansion due to the FWHT zero-padding reduces the mean squared error and improves Recall@10.