Low‑bit quantization can dramatically cut the memory footprint of large language models, yet preserving accuracy while training efficiently remains difficult. Scalar quantization encodes each weight independently, whereas explicit‑codebook vector quantization incurs costly search during training. We therefore introduce E8‑QAT, a 2‑bit quantization‑aware training framework that leverages the $E_8$ lattice as an implicit eight‑dimensional codebook. The approach jointly quantizes weight groups via arithmetic projection, eliminating the need to store or search an explicit codebook in the forward pass. A 2‑bit core encoding combined with a sparse extension exactly preserves the selected lattice points, adding less than 0.1% to index storage. On Qwen3.6‑35B‑A3B, E8‑QAT matches the full‑precision model’s average score across four tasks and, under the same data, schedule, and bit width, improves over the state‑of‑the‑art baseline by 2.03% on IFEval and 1.51% on LiveCodeBench. The 2‑bit representation reduces peak memory by 80% and enables a batch size four times larger; at each representation’s largest feasible batch, E8‑QAT achieves 1.97× the decoding throughput of BF16.
Review: This work highlights the promise of lattice‑based structures for ultra‑low‑bit quantization, offering an efficient path for training massive models.