Toward Multi-Domain and Long-Tailed Quantization via Feature Alignment and Scaling

Post-training quantization (PTQ) is a practical way to reduce the memory footprint of large language models, but low-bit quantization is sensitive to mismatches between the quantization codebook and the empirical weight/activation distributions. We revisit Benford-like leading-digit statistics as a lightweight diagnostic of scale-broad behavior in transformer tensors. Across several model families, we observe a consistent functional dichotomy: transformational nn.Linear weights tend to be Benford-like, whereas LayerNorm parameters systematically deviate. Motivated by this observation, we propose BenQ, a data-free PTQ codebook that uses a simple log-spaced grid as a proxy for scale-broad distributions and applies it selectively to transformational layers while keeping stability-critical parameters in higher precision. In 4-bit group-wise PTQ, BenQ consistently improves over uniform RTN and trades wins with NF4 across architectures and tasks, while remaining substantially simpler than optimization-based methods. We additionally report dynamic activation quantization as an exploratory stress test: the results show that log-spaced grids can reduce RTN failures in some families, but also reveal that outlier handling remains essential for reliable low-bit activation PTQ. Code is available at https://github.com/ufopcsilab/benford-quant.

Post-training quantization (PTQ) compresses large language models by mapping weights to low-bit representations. The scaling factor that defines the quantization grid is typically chosen using simple, data-free heuristics. In this work, we present PiSO (Piecewise Scale Optimization), an algorithm that leverages calibration data to compute the optimal channel-wise weight scales exactly and efficiently under round-to-nearest quantization. PiSO partitions the scale search space into finitely many intervals on which the objective admits a closed-form minimizer. We extend PiSO to group-wise quantization via principled heuristics and propose effective strategies for interleaving scale optimization with error correction. Experiments on Llama and Qwen models across multiple model sizes and target weight bit-widths demonstrate consistent improvements in perplexity and downstream zero-shot accuracy, both standalone and combined with error correction. In particular, we observe increased benefits as the target bit-width narrows and quantization becomes more challenging.

Conventional Post-Training Quantization (PTQ) methods struggle with 4-bit Omni-modal Large Language Models (OLLMs) due to the extreme distribution heterogeneity and disparate outlier patterns across modalities. To address this, we propose MorphoQuant, a modality-aware PTQ framework engineered to preserve cross-modal morphology and mitigate outlier loss. Specifically, we introduce Distribution-Aware Bias Compensation (DABC), which selectively absorbs long-tailed outliers into channel-wise biases. This mechanism safeguards outlier magnitudes while maintaining high-precision discretization for dense inliers, thereby preserving accurate discretization across diverse modal distribution. Complementing this, we propose Morphology-Directed Quantization Function Optimization (MDQFO) to co-optimize the quantization grid with the bias mask, ensuring fine-grained alignment across modalities. Extensive evaluations on Qwen2.5-Omni across benchmarks like MMMU and Video-MME demonstrate our approach's superiority. Notably, our W4A4 model achieves 76.63% on ScienceQA, significantly outperforming SOTA W4A4 methods and surprisingly surpassing the W4A16 baseline, which fully demonstrates the exceptional accuracy-efficiency trade-off of our framework.