arXiv Computation and Language
Sep 11

Structured Transforms for Low-Overhead Quantization of Language Models

The paper revisits Kashin‑decomposition‑based weight quantization for large language models, introducing an improved algorithm that uses a sign‑randomized Discrete Cosine Transform (DCT) instead of a dense random orthogonal matrix. This change reduces per‑iteration cost from ≠(N^2) to ≠(N log N) and, combined with a greedy alternating‑update scheme, guarantees the four‑peak distribution needed for stable 2‑bit clustering while eliminating the need for multi‑restart k‑means. The resulting JAX pipeline, when paired with OPTQ‑style error compensation and QuIP‑style incoherence preprocessing, competes with state‑of‑the‑art quantization methods on OPT, Llama‑2, and Pythia at 4‑bit per channel, and remains numerically stable under stress configurations that cause other methods to diverge.

By Daria Cherniuk, Alexander Rudikov, Boris Kashin, Ivan Oseledets
arXiv Machine Learning
Oct 2

JARQ: Joint Alternating Refinement for Quantization

JARQ is a plug‑in refinement method for group‑wise post‑training quantizers that alternates a joint least‑squares fit of all group scales with bounded Babai proposals to move many codes together on the current grid. It solves a bilinear box‑constrained mixed‑integer least‑squares problem without backpropagation, preserves the host model’s bit width, groups, zero points, and inference cost, and improves accuracy across Llama‑2, Llama‑3, and Qwen models when paired with RTN, GPTQ, OmniQuant, and AWQ hosts. In practice, JARQ reduces perplexity in 90 of 96 comparisons, cuts three‑bit RTN perplexity by up to 36%, raises mean multiple‑choice accuracy in 23 of 24 configurations, and enhances QEP, QuaRot, and OJBKQ outputs, all within under a minute per 7B block.

By Xinyu Wang, Sicheng Lyu, Xiao-Wen Chang