There are 1-bit* LLMs (+1/-1, usually), though they often come with an additional scaling parameter:

https://huggingface.co/prism-ml/Bonsai-27B-gguf#weight-repre...

> Weight Representation: Q1_0_g128 Each weight is a single sign bit: 0 maps to −scale, 1 maps to +scale. Every group of 128 weights shares one FP16 scale factor. > Effective bits per weight: 1.125 (1 sign bit + 16-bit scale amortized over 128 weights)

The Bonsai ternary model also uses this group-wise scaling, so the theoretical bits per parameter is 1.71 instead of ~1.58; additionally, they actually store trits as 2 bits; with the group scaling factor it becomes 2.125 bits/weight: https://huggingface.co/prism-ml/Ternary-Bonsai-27B-gguf#memo...