# Beyond Outliers: A Data-Free Layer-wise Mixed-Precision Quantization Approach Driven by Numerical and Structural Dual-Sensitivity

arXiv: https://arxiv.org/abs/2603.17354 · HTML: https://mlsanity.com/paper/2603.17354/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 30 of 30)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [On the Impact of Calibration Data in Post-training Quantization and Pruning](https://mlsanity.com/paper/2311.09755/) (2023)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)
- [Search What You Want: Barrier Panelty NAS for Mixed Precision Quantization](https://mlsanity.com/paper/2007.10026/) (2020)
- [TreeReview: A Dynamic Tree of Questions Framework for Deep and Efficient LLM-based Scientific Peer Review](https://mlsanity.com/paper/2506.07642/) (2025)
- [Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://mlsanity.com/paper/2501.11110/) (2025)
- [How to Dissect a Muppet: The Structure of Transformer Embedding Spaces](https://mlsanity.com/paper/2206.03529/) (2022)
- [Layer-Wise Quantization: A Pragmatic and Effective Method for Quantizing LLMs Beyond Integer Bit-Levels](https://mlsanity.com/paper/2406.17415/) (2024)
- [UNComp: Can Matrix Entropy Uncover Sparsity? -- A Compressor Design from an Uncertainty-Aware Perspective](https://mlsanity.com/paper/2410.03090/) (2024)
- [Towards Superior Quantization Accuracy: A Layer-sensitive Approach](https://mlsanity.com/paper/2503.06518/) (2025)
- [GuiLoMo: Allocating Expert Number and Rank for LoRA-MoE via Bilevel Optimization with GuidedSelection Vectors](https://mlsanity.com/paper/2506.14646/) (2025)
- [AlignX: Advancing Multilingual Large Language Models with Multilingual Representation Alignment](https://mlsanity.com/paper/2509.24338/) (2025)
- [MixQuant: Mixed Precision Quantization with a Bit-width Optimization Search](https://mlsanity.com/paper/2309.17341/) (2023)
- [LSAQ: Layer-Specific Adaptive Quantization for Large Language Model Deployment](https://mlsanity.com/paper/2412.18135/) (2024)
- [Universality of Layer-Level Entropy-Weighted Quantization Beyond Model Architecture and Size](https://mlsanity.com/paper/2503.04704/) (2025)
- [Training LLMs for Divide-and-Conquer Reasoning Elevates Test-Time Scalability](https://mlsanity.com/paper/2602.02477/) (2026)
- [Intrinsic Structure as a Proxy for Saliency: SVD-Based Weight Preservation for Mixed-Precision Quantization in Large Language Models](https://mlsanity.com/paper/2512.01343/) (2025)

## Built on by (most cited first, 5 of 5)

- [OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond](https://mlsanity.com/paper/2605.19660/) (2026)
- [Massive Activations in Hybrid Linear Attention Large Language Models: Pre-Attention Spikes and Inter-Spike Plateaus](https://mlsanity.com/paper/2608.12149/) (2026)
- [All for 1-Bit: Towards Genuine 1-Bit Post-Training Quantization for LLMs](https://mlsanity.com/paper/2609.06161/) (2026)
- [Efficient Reasoning Exploration via State-Conditioned Latent Steering with Progress Guidance](https://mlsanity.com/paper/2609.24066/) (2026)
- [Quantization Error Is Spectrally Flat: A Single Random Probe Is a Calibrated, Data-Free Sensitivity Estimator, with Application to Budget-Targeted Mixed-Precision Quantization](https://mlsanity.com/paper/2609.33923/) (2026)

## Abstract (arXiv)

Layer-wise mixed-precision quantization (LMPQ) enables effective compression under extreme low-bit settings by allocating higher precision to sensitive layers. However, existing methods typically treat all intra-layer weight modules uniformly and rely on a single numerical property when estimating sensitivity, overlooking their distinct operational roles and structural characteristics. To address this, we propose NSDS, a novel calibration-free LMPQ framework driven by Numerical and Structural Dual-Sensitivity. Specifically, it first mechanistically decomposes each layer into distinct operational roles and quantifies their sensitivity from both numerical and structural perspectives. These dual-aspect scores are then aggregated into a unified layer-wise metric through a robust aggregation scheme based on MAD-Sigmoid and Soft-OR to guide bit allocation. Extensive experiments demonstrate that NSDS consistently achieves superior performance compared to various baselines across diverse models and downstream tasks, without relying on any calibration data.