mlsanityData to 7 Oct 2026

Leech Lattice Vector Quantization for Efficient LLM Compression

arXiv 2603.11021 ↗First posted 11 Mar 2026cs.LGcited by 6

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Abstract (arXiv)

Scalar quantization of large language models (LLMs) is fundamentally limited by information-theoretic bounds. While vector quantization (VQ) overcomes these limits by encoding blocks of parameters jointly, practical implementations must avoid the need for expensive lookup mechanisms or other explicit codebook storage. Lattice approaches address this through highly structured and dense packing. This paper explores the Leech lattice, which, with its optimal sphere packing and kissing configurations at 24 dimensions, is the highest dimensional lattice known with such optimal properties. To make the Leech lattice usable for LLM quantization, we extend an existing search algorithm based on the extended Golay code construction, to i) support indexing, enabling conversion to and from bitstrings without materializing the codebook, ii) allow angular search over union of Leech lattice shells, iii) propose fully-parallelisable dequantization kernel. Lastly, we provide a geometric reinterpretation of combining shape--gain quantization with GPTQ-style Hessian corrections: the standard scale-correction step of shape--gain acts as a retraction onto a product of spheres, yielding a Spherical GPTQ primarily acting on directions. We find that low-angular-distortion LLVQ reduces sensitivity to Hadamard/rotation preprocessing, and enables a strong Hadamard-free PTQ in practice. LLVQ delivers state-of-the-art LLM quantization performance, outperforming recent methods such as Quip#, QTIP, and PVQ. The results highlight the effectiveness of high-dimensional lattices for scalable, theoretically grounded model compression.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 12 of its 30 references that are in the map. First posted on arXiv 11 Mar 2026.

Builds on

12 of 30 references.

References · 12

  1. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,838
  2. 2020Up or Down? Adaptive Rounding for Post-Training Quantizationcited by 600
  3. 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 598
  4. 2023QuIP: 2-Bit Quantization of Large Language Models With Guaranteescited by 397
  5. 2024DataComp-LM: In search of the next generation of training sets for language modelscited by 381
  6. 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 354
  7. 2025SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Modelcited by 307
  8. 2024QTIP: Quantization with Trellises and Incoherence Processingcited by 86
  9. 2024GPTVQ: The Blessing of Dimensionality for LLM Quantizationcited by 78
  10. 2025Model-Preserving Adaptive Roundingcited by 20
  11. 2025FPTQuant: Function-Preserving Transforms for LLM Quantizationcited by 16
  12. 2024Pyramid Vector Quantization for LLMscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Unfolding the Leech Lattice: Fused Multi-Shell Decoding and VRAM Layouts for 2-Bit LLM Weightscited by 1
  2. 2026BiSCo-LLM: Lookup-Free Binary Spherical Coding for Extreme Low-Bit Large Language Model Compressioncited by 0
  3. 2026Disaggregated Quantization: Specializing LLM Prefill and Decodecited by 0
  4. 2026EntroPack: Fast and Accurate Entropy-Coded Weight Compression at Arbitrary Bitratescited by 0
  5. 2026Tetra: Serving Leech-Lattice Quantized LLMs at 2.7 Bits per Parametercited by 0
  6. 2026XOR-Trellis: Ultra-Low-Complexity Dequantization and Curvature-Aware Hadamard-Free LLM Quantizationcited by 0