Original title: Unfolding the Leech Lattice: Fused Multi-Shell Decoding and VRAM Layouts for 2-Bit LLM Weights
Pier-Jean Malandrino · September 2026
Large language models use massive amounts of memory. Squishing their weights down to tiny 2-bit numbers helps them run faster, but decoding complex math codes called Leech lattices is hard. Past tools could only decode one layer, or shell, leaving out the multi-shell system needed for full compression. The researchers built the missing multi-shell decoder to run during model generation at batch 1. They turned the massive codebookA table mapping each short code back to the original group of numbers it represents. into special memory layouts and created a single combined graphics card program to unpack and multiply numbers without slowdowns. They found that stored memory formats act differently than disk formats. Binary bit planes beat one-hot masks, hitting 4.80 bits per weight and 2.15x FP16 speed. End-to-end model speed improved by 1.11x, 1.29x, and 1.41x on 4B, 8B, and 14B models. A 4B model hit 87.0 tok/s in 2.60 GB, while quality losses shrank as models grew.
Imagine compressing all your clothes into labeled bins for a trip. A good system lets you unpack any bin and get back exactly what you packed. Now suppose the best compression method uses 301 different bin labels, but nobody built the instruction manual for unpacking them — you have the bins and the compression ratio, but you cannot retrieve your clothes. In this paper, the researchers write that missing instruction manual and measure how fast it can unpack.
Compressing a language model's weights from 16 bits to 2 bits can shrink its memory footprint by roughly 8x, letting people run large models on much cheaper or smaller hardware. But the mathematically best 2-bit method had a missing piece — nobody had implemented the decoder it actually requires. Without that, the method stays on paper.
The abstract does not evaluate models larger than 14B or tasks beyond perplexity and MMLU. The quality cost is substantial at small sizes — 14.7 MMLU points lost at 4B. All serving measurements are at batch size 1; higher batch sizes are not explored. The comparison shows the Leech approach is slower than the trellis kernel, and the paper does not claim to close that speed gap.
Ask anything about this paper. Answers come from its abstract, and say so when the abstract doesn't cover your question.
Unfolding the Leech Lattice: Fused Multi-Shell Decoding and VRAM Layouts for 2-Bit LLM Weights — Pier-Jean Malandrino
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.