Multi-Bitwidth Quantization for LLMs Using Additive Codebooks

arXiv:2606.12876v2 Announce Type: replace Abstract: As large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints, the ability to adaptively manage the performance-efficiency trade-off without retraining is critical. We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework enabling inference-time precision control over LLM weights from a single quantized model. As theoretical motivation, we prove that Gaussian sources are successively refinable under a weighted mean squared error distortion motivated by LLM loss functions: successive refinement across distortion levels incurs no rate penalty relative to encoding at each level separately. Drop-by-Drop approximates this hierarchical structure in practice by incorporating Matryoshka-style supervision into additive codebook training, inducing an ordering in which codebook prefixes yield accurate partial reconstructions at each precision level. Furthermore, a block-Hadamard rotation brings the weight distribution closer to our Gaussian source assumption. The result is a single model that serves multiple bitwidths by dropping codebooks, reducing storage and quantization cost relative to the static per-bitwidth models. Across Qwen, LLaMA, Gemma, and Mistral, Drop-by-Drop achieves lower perplexity than state-of-the-art multi-bitwidth methods with competitive zero-shot accuracy, while our specialized kernels further reduce decoding latency.

Abstract:As large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints, the ability to adaptively manage the performance-efficiency trade-off without retraining is critical. We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework enabling inference-time precision control over LLM weights from a single quantized model. As theoretical motivation, we prove that Gaussian sources are successively refinable under a weighted mean squared error distortion motivated by LLM loss functions: successive refinement across distortion levels incurs no rate penalty relative to encoding at each level separately. Drop-by-Drop approximates this hierarchical structure in practice by incorporating Matryoshka-style supervision into additive codebook training, inducing an ordering in which codebook prefixes yield accurate partial reconstructions at each precision level. Furthermore, a block-Hadamard rotation brings the weight distribution closer to our Gaussian source assumption. The result is a single model that serves multiple bitwidths by dropping codebooks, reducing storage and quantization cost relative to the static per-bitwidth models. Across Qwen, LLaMA, Gemma, and Mistral, Drop-by-Drop achieves lower perplexity than state-of-the-art multi-bitwidth methods with competitive zero-shot accuracy, while our specialized kernels further reduce decoding latency.

Machine Learning (cs.LG); Computation and Language (cs.CL); Information Theory (cs.IT)

arXiv:2606.12876 [cs.LG]

(or arXiv:2606.12876v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.12876 Focus to learn more arXiv-issued DOI via DataCite

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Multi-Bitwidth Quantization for LLMs Using Additive Codebooks

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