Multi-Bitwidth Quantization for LLMs Using Additive Codebooks

• URL: http://arxiv.org/abs/2606.12876v1
• Date: Thu, 11 Jun 2026 04:06:02 GMT
• Title: Multi-Bitwidth Quantization for LLMs Using Additive Codebooks
• Abstract summary: Large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints.<n>We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework that enables inference-time precision control over LLM weights from a single trained model.
• Score: 12.237109162791091
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints, the ability to adaptively manage the trade-off between performance and efficiency without retraining is critical. We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework that enables inference-time precision control over LLM weights from a single trained model. Our method is theoretically grounded in information theory and successive refinement. We establish that LLM weights, which commonly follow a Gaussian distribution, can be optimally reconstructed with increasing fidelity as additional bits are incorporated, under a weighted mean squared error distortion motivated by LLM loss functions. To realize this in practice, Drop-by-Drop incorporates Matryoshka-style supervision into the loss function, exploiting the structure of additive codebooks. Drop-by-Drop produces a single model where ordered subsets of codebooks yield accurate partial reconstructions at each precision level. This approach significantly reduces storage and memory overhead by allowing a single checkpoint to serve multiple bitwidths, while maintaining competitive perplexity and accuracy across major architectures, such as Qwen, LLaMA, Gemma, and Mistral.

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