# GRINQH: Graded Input-based Quantization Hierarchy for Efficient LLM Generation

arXiv: https://arxiv.org/abs/2606.23419 · HTML: https://mlsanity.com/paper/2606.23419/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Deja Vu: Contextual Sparsity for Efficient LLMs at Inference Time](https://mlsanity.com/paper/2310.17157/) (2023)
- [ReLU Strikes Back: Exploiting Activation Sparsity in Large Language Models](https://mlsanity.com/paper/2310.04564/) (2023)
- [Pretraining Large Language Models with NVFP4](https://mlsanity.com/paper/2509.25149/) (2025)
- [Training-Free Activation Sparsity in Large Language Models](https://mlsanity.com/paper/2408.14690/) (2024)
- [Any-Precision LLM: Low-Cost Deployment of Multiple, Different-Sized LLMs](https://mlsanity.com/paper/2402.10517/) (2024)
- [MARLIN: Mixed-Precision Auto-Regressive Parallel Inference on Large Language Models](https://mlsanity.com/paper/2408.11743/) (2024)
- [Optimize Weight Rounding via Signed Gradient Descent for the Quantization of LLMs](https://mlsanity.com/paper/2309.05516/) (2023)
- [ProSparse: Introducing and Enhancing Intrinsic Activation Sparsity within Large Language Models](https://mlsanity.com/paper/2402.13516/) (2024)
- [TorchAO: PyTorch-Native Training-to-Serving Model Optimization](https://mlsanity.com/paper/2507.16099/) (2025)
- [Progressive Mixed-Precision Decoding for Efficient LLM Inference](https://mlsanity.com/paper/2410.13461/) (2024)

## Built on by (most cited first, 1 of 1)

- [Activation Sparsity with Weight Approximation for Faster LLM Decoding on Offloaded Weights](https://mlsanity.com/paper/2610.02598/) (2026)

## Abstract (arXiv)

Autoregressive decoding with LLMs is primarily bottlenecked by GPU memory bandwidth, especially in edge-computing settings. While quantization is essential for mitigating this bottleneck, most existing methods treat inference as a uniform process and fail to account for the asymmetry between the compute-bound prefill stage and the memory-bound decoding stage. We propose GRINQH (GRaded INput-based Quantization Hierarchy), a weight-only post-training quantization framework that accelerates decoding by unifying quantization and sparsification. GRINQH leverages activation magnitudes as a proxy for computational importance to dynamically assign weight channels to different precision levels, enabling flexible average bit widths during decoding. Evaluated on Llama3 and Qwen3 models, GRINQH outperforms state-of-the-art fixed- and mixed-precision baselines at comparable 3- and 4-bit settings, even enabling effective 2-bit generation. We experimentally verify theoretical speedups by leveraging a hierarchical nested memory layout for multi-precision storage in a custom GPU kernel. Ultimately, GRINQH establishes a new state-of-the-art Pareto frontier for LLM generation, enabling a dynamic trade-off between generation quality and inference speed.