GoQuant: Geometric Orthogonal Residual Projection for Multiplier-Free Power-of-Two Transformer Quantization

The deployment of Large Language Models (LLMs) and Vision Transformers (ViTs) on edge devices is significantly constrained by memory capacity 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 general multiplications in the dominant dot-product computation with bit-shift operations. However, its non-uniform exponential lattice inherently suffers from a Low Angular Resolution Regime, a structural limitation that becomes particularly pronounced below 4-bit precision and can substantially degrade the representation of high-dimensional feature manifolds. To address this geometric limitation, we propose Geometric Orthogonal Residual Projection Quantization (GoQuant), an algorithm--hardware co-design framework for multiplier-reduced low-bit inference. By formulating quantization as a dual-basis geometric projection, GoQuant constructs a higher-resolution residual lattice while retaining a shift-and-add inner-product structure. Its analytical solver further avoids computationally intensive gradient-based or iterative search procedures. The data-free Geometric-Only (GEO) mode quantizes LLaMA-2-7B in only 0.47 minutes, while the Activation-Refined (REF) mode completes full-model quantization in approximately 4.4 minutes.