OA-EM (Output-Aware Expectation-Maximisation) is a Hessian-weighted EM algorithm that significantly improves codebook initialization for additive quantization, particularly at extreme compression rates. See our paper for details.

Quantization Details

Parameter	Value
Method	AQLM + OA-EM init + PV-tuning
Bitrate	2 bpp (2 codebooks × 8-bit, group size 8)
Codebook config	`num_codebooks=2, nbits_per_codebook=8, in_group_size=8`
Beam size	8
OA-EM config	3 rounds, 100 Adam steps, lr=1e-4
PV-tuning	5 epochs, LAMB optimizer, lr=3e-4, 10K C4 samples
Seed	42
Context length	4096 tokens

Results

Perplexity

Model	Pre-PV Wiki-2	Pre-PV C4	Post-PV Wiki-2	Post-PV C4
AQLM Greedy	18.86	15.01	9.39	12.02
AQLM OA-EM	16.38	14.50	9.25	11.89

Downstream Tasks (post-PV-tuning, b=8)

Task	Metric	AQLM Greedy	AQLM OA-EM
ARC-Challenge	acc_norm ↑	.432	.424
ARC-Easy	acc_norm ↑	.656	.677
HellaSwag	acc_norm ↑	.707	.714
LAMBADA	acc ↑	.679	.675
LAMBADA	ppl ↓	4.60	4.59
PIQA	acc_norm ↑	.759	.769
WinoGrande	acc ↑	.661	.679
Average		.649	.656

Usage

python

from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained(
    "kennedyian94/Llama-3.1-8B-AQLM-OA-EM-2Bit-2x8",
    trust_remote_code=True,
    torch_dtype="auto",
    device_map="auto"
)
tokenizer = AutoTokenizer.from_pretrained("kennedyian94/Llama-3.1-8B-AQLM-OA-EM-2Bit-2x8")

inputs = tokenizer("The meaning of life is", return_tensors="pt").to(model.device)
outputs = model.generate(**inputs, max_new_tokens=100)
print(tokenizer.decode(outputs[0], skip_special_tokens=True))

Note: Requires the aqlm inference library:

pip install aqlm[gpu]

Paper

Initialisation Determines the Basin: Efficient Codebook Optimisation for Extreme LLM Quantization

Ian W. Kennedy and Nafise Sadat Moosavi, University of Sheffield

arXiv:2604.08118 | Code

Citation

bibtex

@article{kennedy2026oaem,
  title={Initialisation Determines the Basin: Efficient Codebook Optimisation for Extreme LLM Quantization},
  author={Kennedy, Ian W. and Moosavi, Nafise Sadat},
  journal={arXiv preprint arXiv:2604.08118},
  year={2026}
}

mariokart59/Llama-3.1-8B-AQLM-OA-EM-2Bit-2x8

Llama-3.1-8B-AQLM-OA-EM-2Bit-2x8