Unfolding the Leech Lattice: Fused Multi-Shell Decoding and VRAM Layouts for 2-Bit LLM Weights
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Abstract (arXiv)
Leech-lattice vector quantization holds the strongest reported 2-bit quality under its own evaluation protocol. Its kernel decodes one shell; we found no implementation of the multi-shell decoder the rate requires. This paper supplies one and measures its serving cost for decode-phase GEMV at batch 1. First, a serving path for the full 301-class codebook: an offline expansion into GPU layouts and a fused dequantize-plus-matvec kernel reading them without warp divergence, verified against f64. Second, the in-VRAM rate is a design axis distinct from the on-disk rate. Four bit-exact layouts timed in one process show binary bit planes beating one-hot masks on size and speed at constant bandwidth (4.80 bits per weight, 2.15x FP16). Below 4.3 bits a second, irregular stream enters; at 3.6 the decode stops being shifts and masks. Third, deployed four-bit (AWQ) and two-bit (QTIP) GEMV kernels run in the same process. The trellis kernel reads 2.40x fewer bytes than our served layout and runs 2.27x faster at near-equal fractions of their byte bounds: the time gap tracks the traffic gap, the price of unfolding a codebook too large for a lookup table. Fourth, the validity envelope: the trellis kernel outruns our no-weights control, so our launch geometry sets that floor, and on a second memory hierarchy every lattice arm falls below FP16. With the output head held identical across arms, the kernel-and-format path gains 1.11x, 1.29x and 1.41x end to end at 4B, 8B and 14B; with an int8 output head the served 4B reaches 87.0 tok/s in 2.60 GB. The quality cost, 1.38x perplexity and 14.7 MMLU points at 4B, shrinks across the three sizes measured.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 14 of its 30 references that are in the map. First posted on arXiv 2 Sep 2026.
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References · 14
- 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,599
- 2020Measuring Massive Multitask Language Understandingcited by 7,963
- 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
- 2016Pointer Sentinel Mixture Modelscited by 3,096
- 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,919
- 2023AWQ: Activation-aware Weight Quantization for LLM Compression and Accelerationcited by 1,298
- 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 634
- 2024SpinQuant: LLM quantization with learned rotationscited by 471
- 2023QuIP: 2-Bit Quantization of Large Language Models With Guaranteescited by 414
- 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 378
- 2023SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compressioncited by 367
- 2024Extreme Compression of Large Language Models via Additive Quantizationcited by 232
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- 2026GRINQH: Graded Input-based Quantization Hierarchy for Efficient LLM Generation
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- 2026TurboAngle: Near-Lossless KV Cache Compression via Uniform Angle Quantization
- 2026BCJR-QAT: A Differentiable Relaxation of Trellis-Coded Weight Quantization