mlsanityData to 14 Oct 2026

Grid Games: The Power of Multiple Grids for Quantizing Large Language Models

arXiv 2605.12327 ↗First posted 12 May 2026cs.LGcited by 2

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Abstract (arXiv)

A major recent advance in quantization is given by microscaled 4-bit formats such as NVFP4 and MXFP4, quantizing values into small groups sharing a scale, assuming a fixed floating-point grid. In this paper, we study the following natural extension: assume that, for each group of values, we are free to select the "better" among two or more 4-bit grids marked by one or more bits in the scale value. We formalize the power-of-two-grids (PO2) problem, and provide theoretical results showing that practical small-group formats such as MXFP or NVFP can benefit significantly from PO2 grids, while the advantage vanishes for very large groups. On the practical side, we instantiate several grid families, including 1) PO2(NF4), which pairs the standard NF4 normal grid with a learned grid, 2) MPO2, a grid pair that is fully learned over real weights and activations, 3) PO2(Split87), an explicit-zero asymmetric grid and 4) SFP4, a TensorCore-implementable triple which pairs NVFP4 with two shifted variants. Results for post-training quantization of standard open models and pre-training of Llama-like models show that adaptive grids consistently improve accuracy vs single-grid FP4 under both weight-only and weight+activation. Source code is available at https://github.com/IST-DASLab/GridGames.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 28 of its 40 references that are in the map. First posted on arXiv 12 May 2026.

Builds on

28 of 40 references.

References · 28

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  3. 2025Qwen3 Technical Reportcited by 8,820
  4. 2020Measuring Massive Multitask Language Understandingcited by 7,963
  5. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,886
  6. 2019HellaSwag: Can a Machine Really Finish Your Sentence?cited by 4,100
  7. 2023QLoRA: Efficient Finetuning of Quantized LLMscited by 3,418
  8. 2019PIQA: Reasoning about Physical Commonsense in Natural Languagecited by 2,883
  9. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,919
  10. 2023Instruction-Following Evaluation for Large Language Modelscited by 1,228
  11. 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 634
  12. 2021A White Paper on Neural Network Quantizationcited by 472
16 more
  1. 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 378
  2. 2023SqueezeLLM: Dense-and-Sparse Quantizationcited by 294
  3. 2018Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learningcited by 215
  4. 2023Microscaling Data Formats for Deep Learningcited by 152
  5. 2024QTIP: Quantization with Trellises and Incoherence Processingcited by 91
  6. 2025FP4 All the Way: Fully Quantized Training of LLMscited by 40
  7. 2025Quartet: Native FP4 Training Can Be Optimal for Large Language Modelscited by 39
  8. 2025Training LLMs with MXFP4cited by 37
  9. 2025Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scalingcited by 35
  10. 2024Fast Matrix Multiplications for Lookup Table-Quantized LLMscited by 29
  11. 2025QuEST: Stable Training of LLMs with 1-Bit Weights and Activationscited by 22
  12. 2026Quartet II: Accurate LLM Pre-Training in NVFP4 by Improved Unbiased Gradient Estimationcited by 21
  13. 2026Statistically-Lossless Quantization of Large Language Modelscited by 6
  14. 2025Improving Block-Wise LLM Quantization by 4-bit Block-Wise Optimal Float (BOF4): Analysis and Variationscited by 5
  15. 2024Towards Cheaper Inference in Deep Networks with Lower Bit-Width Accumulatorscited by 4
  16. 2026Adaptive Block-Scaled Data Typescited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026A Hardware-Aware, Per-Layer Methodology for Post-Training Quantization of Large Language Modelscited by 0
  2. 2026Disaggregated Quantization: Specializing LLM Prefill and Decodecited by 0

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  1. 2025Bridging the Gap Between Promise and Performance for Microscaling FP4 Quantization
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  3. 2025PoTPTQ: A Two-step Power-of-Two Post-training for LLMs
  4. 2025MicroMix: Efficient Mixed-Precision Quantization with Microscaling Formats for Large Language Models
  5. 2026BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models
  6. 2023Integer or Floating Point? New Outlooks for Low-Bit Quantization on Large Language Models
  7. 2026Two-Stage Grid Optimization for Group-wise Quantization of LLMs
  8. 2025any4: Learned 4-bit Numeric Representation for LLMs