All for 1-Bit: Towards Genuine 1-Bit Post-Training Quantization for LLMs

• URL: http://arxiv.org/abs/2609.06161v1
• Date: Sat, 05 Sep 2026 16:03:41 GMT
• Title: All for 1-Bit: Towards Genuine 1-Bit Post-Training Quantization for LLMs
• Abstract summary: All for 1-Bit (AF1) is a genuine 1-bit PTQ framework for large language models.<n> AF1 consistently outperforms existing binarization-based PTQ methods in perplexity and zero-shot accuracy.
• Score: 11.08932160665543
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models (LLMs) have achieved remarkable progress, yet their massive storage and memory-bandwidth demands still hinder efficient deployment. Weight binarization is a promising solution, but existing binarization-based post-training quantization (PTQ) methods usually far exceed the nominal 1-bit storage target due to hidden overhead. To address this gap, we propose All for 1-Bit (AF1), a genuine 1-bit PTQ framework for LLMs. AF1 comprises two complementary components: (1) Null-space-Aware Binary Factorization (NABF) for improving binary reconstruction through Hessian-aware surrogate reparameterization, null-space-aware binary factorization, and scale-only global reconstruction; and (2) Hierarchical Shapley Allocation (HiSA) for assigning structural capacity using hierarchical Shapley sensitivity. Together, they preserve model accuracy under a strict 1.0-BPW budget in the PTQ setting. Experiments on LLaMA, Qwen, and Gemma families show that AF1 consistently outperforms existing binarization-based PTQ methods in perplexity and zero-shot accuracy. Compared with BF16, AF1 achieves an average 2.5 times inference speedup and over 90% memory reduction across evaluated models, providing a practical path toward deployable genuine 1-bit compression for LLMs. The code for reproducibility is available at https://github.com/Kishon-zzx/AF1.

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