Multi-Bitwidth Quantization for LLMs Using Additive Codebooks
This work addresses the need for adaptive precision in LLM deployment on heterogeneous hardware without retraining, offering a practical solution for resource-constrained environments.
Drop-by-Drop enables inference-time precision control over LLM weights from a single trained model, achieving competitive perplexity and accuracy across architectures like Qwen, LLaMA, Gemma, and Mistral while reducing storage overhead.
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.