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

arXiv: https://arxiv.org/abs/2609.06161 · HTML: https://mlsanity.com/paper/2609.06161/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 63 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 30 of 41)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Atom: Low-bit Quantization for Efficient and Accurate LLM Serving](https://mlsanity.com/paper/2310.19102/) (2023)
- [AlphaEdit: Null-Space Constrained Knowledge Editing for Language Models](https://mlsanity.com/paper/2410.02355/) (2024)
- [BiLLM: Pushing the Limit of Post-Training Quantization for LLMs](https://mlsanity.com/paper/2402.04291/) (2024)
- [Training Networks in Null Space of Feature Covariance for Continual Learning](https://mlsanity.com/paper/2103.07113/) (2021)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [MedEyes: Learning Dynamic Visual Focus for Medical Progressive Diagnosis](https://mlsanity.com/paper/2511.22018/) (2025)
- [ReCreate: Reasoning and Creating Domain Agents Driven by Experience](https://mlsanity.com/paper/2601.11100/) (2026)
- [Pathology-Aware Prototype Evolution via LLM-Driven Semantic Disambiguation for Multicenter Diabetic Retinopathy Diagnosis](https://mlsanity.com/paper/2511.22033/) (2025)
- [Towards Effective Data-Free Knowledge Distillation via Diverse Diffusion Augmentation](https://mlsanity.com/paper/2410.17606/) (2024)
- [Scheduling Your LLM Reinforcement Learning with Reasoning Trees](https://mlsanity.com/paper/2510.24832/) (2025)
- [MedSynapse-V: Bridging Visual Perception and Clinical Intuition via Latent Memory Evolution](https://mlsanity.com/paper/2604.26283/) (2026)
- [SQLForge: Synthesizing Reliable and Diverse Data to Enhance Text-to-SQL Reasoning in LLMs](https://mlsanity.com/paper/2505.13725/) (2025)
- [LittleBit: Ultra Low-Bit Quantization via Latent Factorization](https://mlsanity.com/paper/2506.13771/) (2025)
- [QUARK: Quantization-Enabled Circuit Sharing for Transformer Acceleration by Exploiting Common Patterns in Nonlinear Operations](https://mlsanity.com/paper/2511.06767/) (2025)
- [Fixed Anchors Are Not Enough: Dynamic Retrieval and Persistent Homology for Dataset Distillation](https://mlsanity.com/paper/2602.24144/) (2026)
- [When TableQA Meets Noise: A Dual Denoising Framework for Complex Questions and Large-scale Tables](https://mlsanity.com/paper/2509.17680/) (2025)
- [SpecQuant: Spectral Decomposition and Adaptive Truncation for Ultra-Low-Bit LLMs Quantization](https://mlsanity.com/paper/2511.11663/) (2025)
- [RobuQ: Pushing DiTs to W1.58A2 via Robust Activation Quantization](https://mlsanity.com/paper/2509.23582/) (2025)
- [Rethinking Table Pruning in TableQA: From Sequential Revisions to Gold Trajectory-Supervised Parallel Search](https://mlsanity.com/paper/2601.03851/) (2026)

## Built on by (most cited first, 2 of 2)

- [JustQuant: You Don't Need Smoothing, SVD, or Rotation for 4-Bit Activation Quantization](https://mlsanity.com/paper/2609.33601/) (2026)
- [LoopQuant: Accurate and Efficient Post-Training Quantization for Looped Transformers](https://mlsanity.com/paper/2610.16368/) (2026)

## Abstract (arXiv)

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.