SLQ quantizes LLMs to 3.3 bits per parameter and still speeds up inference

TheZachMueller · x · 2026-07-24

Statistically-lossless quantization reaches 3.3 bits per parameter

This paper proposes SLQ (Statistically-Lossless Quantization) for large language models and argues that quantization does not have to force a trade-off between fidelity and speed.

Task-lossless compression preserves zero-shot benchmark accuracy within natural sampling variance and can be achieved at aggressive bit widths.
Distribution-lossless compression is defined more strictly: the quantized model’s next-token distribution should be practically indistinguishable from the original.
The authors introduce Expected Acceptance Rate (EAR) as an interpretable fidelity metric; for example, EAR ≥ 0.99 implies 99% token agreement under optimal coupling.
They prove a variance law showing symmetric quantization inflates noise variance by γ² relative to asymmetric quantization.
With SLQ, they report task-lossless compression below 4 bpp (as low as 3.3 bits/parameter, model-dependent), distribution-lossless compression at 5–6 bpp, and 1.7–3.6× inference speedups versus FP16 using optimized kernels.

The code is published at github.com/IST-DASLab/SLQ.

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SLQ quantizes LLMs to 3.3 bits per parameter and still speeds up inference

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