# Leech Lattice Vector Quantization for Efficient LLM Compression

arXiv: https://arxiv.org/abs/2603.11021 · HTML: https://mlsanity.com/paper/2603.11021/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [QTIP: Quantization with Trellises and Incoherence Processing](https://mlsanity.com/paper/2406.11235/) (2024)
- [GPTVQ: The Blessing of Dimensionality for LLM Quantization](https://mlsanity.com/paper/2402.15319/) (2024)
- [Model-Preserving Adaptive Rounding](https://mlsanity.com/paper/2505.22988/) (2025)
- [FPTQuant: Function-Preserving Transforms for LLM Quantization](https://mlsanity.com/paper/2506.04985/) (2025)
- [Pyramid Vector Quantization for LLMs](https://mlsanity.com/paper/2410.16926/) (2024)

## Built on by (most cited first, 7 of 7)

- [Unfolding the Leech Lattice: Fused Multi-Shell Decoding and VRAM Layouts for 2-Bit LLM Weights](https://mlsanity.com/paper/2609.02652/) (2026)
- [BiSCo-LLM: Lookup-Free Binary Spherical Coding for Extreme Low-Bit Large Language Model Compression](https://mlsanity.com/paper/2607.08643/) (2026)
- [Disaggregated Quantization: Specializing LLM Prefill and Decode](https://mlsanity.com/paper/2609.26333/) (2026)
- [EntroPack: Fast and Accurate Entropy-Coded Weight Compression at Arbitrary Bitrates](https://mlsanity.com/paper/2609.34185/) (2026)
- [Tetra: Serving Leech-Lattice Quantized LLMs at 2.7 Bits per Parameter](https://mlsanity.com/paper/2609.35465/) (2026)
- [XOR-Trellis: Ultra-Low-Complexity Dequantization and Curvature-Aware Hadamard-Free LLM Quantization](https://mlsanity.com/paper/2610.00432/) (2026)
- [SAGE: Pushing 2-Bit Vector-Quantized LLMs toward Real-World Usability](https://mlsanity.com/paper/2610.14745/) (2026)

## 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.