mlsanityData to 14 Oct 2026

Transforms for LLM Quantization: The Great Inversion and Format Co-Design

arXiv 2608.25188 ↗First posted 25 Aug 2026cs.LG cs.IT math.ITcited by 0

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Abstract (arXiv)

Most competitive 4-bit LLM research pipelines now open the same way: apply a linear, function-preserving transform (rotation, scaling, permutation, non-orthogonal affine) so the outlier mass sits more favorably against the group scales, and only then round. Yet we are aware of no survey dedicated to this transform stage, and its literature is quietly re-deriving an older theory. We identify and formalize the principle that organizes it, the Great Inversion: allocation-flexible coding rewards energy concentration, whereas the grouped shared-scale quantization a deployed matrix instruction performs rewards within-group flattening. Classical transform coding (1963: decorrelate, allocate bits, quantize) spends different bits per coordinate at a fixed total rate; for a Gaussian source at high rate the Karhunen-Loeve transform's concentration minimizes distortion. A deployed operand tile instead carries one absolute-maximum scale per group and equal bits everywhere, with no allocation; on a uniform grid that objective rewards flattening, approached by Hadamard incoherence. We prove that opposition under within-group majorization: the prescriptions point in opposite directions, each backed by a proof against its own objective, and for a generic spectrum no optimality guarantee transfers. A second axis is the number format: the non-uniform FP4 grid makes flattening buy less, MXFP4's power-of-two block scale still rewards a rotation confined to that block, and NVFP4's mantissa-carrying scale largely removes that pull, so the target pole depends jointly on allocation regime and format. We survey 200 works to a June 2026 cutoff; classify 43 transform methods by structure, data-awareness, searched-versus-constructed, and runtime cost; record, where reported, how they compose with GPTQ rounding; distill a first-choice guide by deployment regime; and close with the open problems it exposes.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 56 of its 200 references that are in the map. First posted on arXiv 25 Aug 2026.

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References · 56

  1. 2020GLU Variants Improve Transformercited by 1,804
  2. 2023ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Modelscited by 169
  3. 2023Microscaling Data Formats for Deep Learningcited by 152
  4. 2025TurboQuant: Online Vector Quantization with Near-optimal Distortion Ratecited by 125
  5. 2023RPTQ: Reorder-based Post-training Quantization for Large Language Modelscited by 116
  6. 2024GPTVQ: The Blessing of Dimensionality for LLM Quantizationcited by 82
  7. 2025Pretraining Large Language Models with NVFP4cited by 76
  8. 2025Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scalingcited by 35
  9. 2024A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithmscited by 31
  10. 2025Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantizationcited by 28
  11. 2025PolarQuant: Quantizing KV Caches with Polar Transformationcited by 27
  12. 2025NestQuant: Nested Lattice Quantization for Matrix Products and LLMscited by 23
38 more
  1. 2024Pushing the Limits of Large Language Model Quantization via the Linearity Theoremcited by 21
  2. 2026Quartet II: Accurate LLM Pre-Training in NVFP4 by Improved Unbiased Gradient Estimationcited by 21
  3. 2025Block Rotation is All You Need for MXFP4 Quantizationcited by 20
  4. 2025INT v.s. FP: A Comprehensive Study of Fine-Grained Low-bit Quantization Formatscited by 18
  5. 2024QQQ: Quality Quattuor-Bit Quantization for Large Language Modelscited by 16
  6. 2025Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronoscited by 16
  7. 2024Optimal Quantization for Matrix Multiplicationcited by 14
  8. 2024NeuZip: Memory-Efficient Training and Inference with Dynamic Compression of Neural Networkscited by 14
  9. 2024HadaCore: Tensor Core Accelerated Hadamard Transform Kernelcited by 12
  10. 2025LRQ-DiT: Log-Rotation Post-Training Quantization of Diffusion Transformers for Image and Video Generationcited by 12
  11. 2026Pushing the Limits of Block Rotations in Post-Training Quantizationcited by 11
  12. 2026HiFloat4 Format for Language Model Inferencecited by 11
  13. 2025ButterflyQuant: Ultra-low-bit LLM Quantization through Learnable Orthogonal Butterfly Transformscited by 10
  14. 2025KVLinC : KV Cache Quantization with Hadamard Rotation and Linear Correctioncited by 10
  15. 2026Benchmarking Post-Training Quantization of Large Language Models under Microscaling Floating Point Formatscited by 10
  16. 2023TEQ: Trainable Equivalent Transformation for Quantization of LLMscited by 9
  17. 2025Huff-LLM: End-to-End Lossless Compression for Efficient LLM Inferencecited by 9
  18. 2026OSCAR: Offline Spectral Covariance-Aware Rotation for 2-bit KV Cache Quantizationcited by 9
  19. 2026Provable Quantization with Randomized Hadamard Transformcited by 8
  20. 2025PCDVQ: Enhancing Vector Quantization for Large Language Models via Polar Coordinate Decouplingcited by 7
  21. 2025HadaNorm: Diffusion Transformer Quantization through Mean-Centered Transformationscited by 7
  22. 2025ConvRot: Rotation-Based Plug-and-Play 4-bit Quantization for Diffusion Transformerscited by 7
  23. 2026High-Rate Quantized Matrix Multiplication Icited by 7
  24. 2026Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Provencited by 6
  25. 2023SmoothQuant+: Accurate and Efficient 4-bit Post-Training WeightQuantization for LLMcited by 5
  26. 2024Rotated Runtime Smooth: Training-Free Activation Smoother for accurate INT4 inferencecited by 5
  27. 2025BASE-Q: Bias and Asymmetric Scaling Enhanced Rotational Quantization for Large Language Modelscited by 5
  28. 2026Dissecting Quantization Error: A Concentration-Alignment Perspectivecited by 5
  29. 2026HiFloat4 Format for Language Model Pre-training on Ascend NPUscited by 5
  30. 2026DiRotQ: Rotation-Aware Quantization for 4-bit Diffusion Transformerscited by 5
  31. 2026HARP: Hadamard-Preconditioned Adaptive Rotation Processor for Extreme LLM Quantizationcited by 5
  32. 2025MergeQuant: Accurate 4-bit Static Quantization of Large Language Models by Channel-wise Calibrationcited by 4
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  37. 2025A Comprehensive Evaluation on Quantization Techniques for Large Language Modelscited by 3
  38. 2026TORQ: Two-Level Orthogonal Rotation for MXFP4 Quantizationcited by 3

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