Lossless quantization has usually meant giving up inference speedup. This paper changes that. SLQ (Statistically-Lossless Quantization) reaches task-lossless compression at 3.3 bits per parameter, and distribution-lossless at 5-6 bpp where the output distribution is practically indistinguishable from the original. 1.7 to 3.6x throughput over BF16 in @vllm_project. Beats FP8 while staying lossless. From Michael Helcig, @_EldarKurtic, and @DAlistarh.