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

The deployment of Large Language Models (LLMs) and Vision Transformers (ViTs) on edge devices is significantly constrained by memory limitations and the critical timing bottlenecks introduced by dense Multiply-Accumulate (MAC) arrays. In the ultra-low bit regime, logarithmic Power-of-Two (PoT) quantization provides a hardware-efficient alternative by replacing MAC operations with bit-shifts. However, the non-uniform exponential lattice is inherently limited by a \textbf{Low Angular Resolution Regime}, a structural flaw that becomes particularly pronounced at sub-4-bit thresholds, leading to a notable degradation of high-dimensional feature manifolds. To address this geometric limitation, we propose Geometric Orthogonal Residual Projection Quantization (GoQuant), an algorithm-hardware co-design framework. By formulating quantization as a dual-basis geometric projection, GoQuant adaptively synthesizes a higher-resolution residual lattice using strictly shift-and-add operations. Furthermore, its analytical solver offers a practical alternative to computationally intensive gradient-based optimization, reducing the full-model calibration time for LLaMA-2-7B to approximately 15 minutes. Extensive evaluations demonstrate GoQuant's applicability across modalities and its hardware efficiency. Under the 3-bit (W3/A16) constraint, it achieves a perplexity of 6.10 on LLaMA-2-7B, comparing favorably to conventional MAC-intensive baselines like AWQ without relying on asymmetric scaling, while maintaining competitive accuracy in 4-bit scenarios. At the silicon level, standard-cell RTL synthesis at a 28nm node indicates that GoQuant effectively mitigates the timing bottlenecks associated with dense multiplier trees. By flattening the combinational logic depth, our parallel shift-and-add datapath reduces the critical path delay to 0.35 ns.

Quantization is essential for efficient large language model (LLM) inference, yet the dequantization step-converting low-bit weights back to high-precision for matrix multiplication has become a critical bottleneck on modern AI accelerators. On architectures with decoupled compute units (e.g., Ascend NPUs), dequantization operations can consume more cycles than the matrix multiplication itself, leaving the high-throughput tensor cores underutilized. This paper presents Multi-Scale Dequant (MSD), a quantization framework that removes weight/KV dequantization from the GEMM critical path. Instead of lifting low-bit weights to BF16 precision, MSD decomposes high-precision BF16 activations into multiple low-precision components, each of which can be multiplied directly with quantized weights via native hardware-accelerated GEMM. This approach shifts the computational paradigm from precision conversion to multi-scale approximation, avoiding INT8-to-BF16 weight conversion before GEMM. We instantiate MSD for two weight formats and derive tight error bounds for each. For INT8 weights (W4A16), two-pass INT8 decomposition achieves near 16 effective bits. For MXFP4 weights (W4A16), two-pass MXFP4 decomposition yields near 6.6 effective bits with error bound 1/64 per block surpassing single-pass MXFP8(5.24 bits) while maintaining the same effective GEMM compute time. We further derive closed-form latency and HBM traffic models showing that MSD avoids the Vector-Cube pipeline stall caused by dequantization and reduces KV cache HBM traffic by up to 2.5 times in attention. Numerical simulations on matrix multiplication and Flash Attention kernels confirm that MSD does not degrade accuracy compared to dequantization baselines, and in many settings achieves lower L2 error.

Vector quantization is a fundamental primitive for scalable machine learning systems, enabling memory-efficient storage, fast retrieval, and compressed inference. Recent rotation-based quantizers such as EDEN, RabitQ, and TurboQuant have introduced strong guarantees and empirical performance, but the surrounding comparisons have been difficult to interpret because they rely on different distortion criteria, probability regimes, and implementation assumptions. As our first contribution, we provide a unified theoretical comparison of these methods and show that their relative advantages are criterion-dependent rather than absolute: EDEN and TurboQuant are favorable for MSE distortion, EDEN is also effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison further clarifies that EDEN provides particularly strong guarantees for expected distortion measures. As our second contribution, we introduce Block-Sphere Quantization (BlockQuant), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, BlockQuant quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design theoretically improves over the baselines considered in this paper for both reconstruction MSE and expected inner-product distortion. Our experiments on real embedding datasets and long-context LLM inference tasks show practical gains that are consistent with our theoretical improvements.