Initialisation Determines the Basin: Efficient Codebook Optimisation for Extreme LLM Quantization
This addresses the challenge of deploying large language models on edge devices through extreme compression, though it appears incremental as it improves an existing quantization method rather than introducing a new paradigm.
The paper tackles the problem of catastrophic failure in extreme 2-bit LLM quantization by identifying codebook initialization as the dominant bottleneck, and proposes OA-EM initialization which consistently produces better solutions across architectures and compression rates, improving perplexity by orders of magnitude at 2 bpp.
Additive quantization enables extreme LLM compression with O(1) lookup-table dequantization, making it attractive for edge deployment. Yet at 2-bit precision, it often fails catastrophically, even with extensive search and finetuning. We show that the dominant bottleneck is codebook initialisation. Greedy sequential initialisation frequently places the model in poor optimisation regions that subsequent beam search and PV-tuning struggle to overcome. We analyse this behaviour through the representational ratio \r{ho} = N/KM, which characterises the relationship between weight groups and codebook capacity, and propose OA-EM, an output-aware EM initialisation method using Hessian-weighted Mahalanobis distance. Across compression rates, search budgets, and three architectures (Llama 3.2 3B, Llama 3.1 8B, Qwen 2.5 3B), OA-EM consistently produces better solutions after PV-tuning and dominates the quality-compute frontier. The severity of the bottleneck scales with \r{ho}: moderate at 3 bpp but extreme at 2 bpp, where poor initialisation can degrade perplexity by orders of magnitude. More broadly, our results highlight the importance of optimisation geometry in compressed model spaces, where initialisation can dominate subsequent search and fine-tuning.