Multi-Bitwidth Quantization for LLMs Using Additive Codebooks

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.