Large Language Models (LLMs) face deployment challenges due to high computational costs, and while Post-Training Quantization (PTQ) offers a solution, existing rotation-based methods struggle at very low bit-widths like 2-bit. We introduce a novel, training-free approach to construct an improved rotation matrix, addressing the limitations of current methods. The key contributions include leveraging the Walsh-Hadamard transform with sequency ordering, which clusters similar frequency components to reduce quantization error compared to standard Hadamard matrices, significantly improving performance. Furthermore, we propose a Grouped Sequency-arranged Rotation (GSR) using block-diagonal matrices with smaller Walsh blocks, effectively isolating outlier impacts and achieving performance comparable to optimization-based methods without requiring any training. Our method demonstrates robust performance on reasoning tasks and Perplexity (PPL) score on WikiText-2. Our method also enhances results even when applied over existing learned rotation techniques.

We propose Rotate, Clip, and Partition (RCP), a Quantization-Aware Training (QAT) approach that first realizes extreme compression of LLMs with W2A4KV4 (2-bit weight, 4-bit activation, and 4-bit KV-cache) configuration. RCP integrates recent rotation techniques with a novel non-uniform weight quantizer design by theoretically and empirically analyzing the impact of rotation on the non-uniformity of weight distribution. Our weight quantizer, Learnable Direct Partitioning (LDP), introduces learnable parameters to directly learn non-uniform intervals jointly with LLM weights. We also present a GPU kernel supporting GEMV on non-uniform W2A4 as proof of concept. Experiments show that RCP can compress LLaMA-2-7B to W2A4KV4 with a loss of only 2.84 WikiText2 PPL and 5.29 times reduced memory footprint. Furthermore, RCP can quantize challenging mobile-targeted LLaMA-3.2 models and domain-specific WizardCoder-7B and MetaMath-7B with no critical problems such as convergence failure and repetition. Code is available at https://github.com/songsm921/RCP.