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.
Figures & tables
Figure 1: Accuracy–memory trade-off across BF16 models and binarization-based PTQ methods, with L, G, and Q denoting LLaMA-3, Gemma-3, and Qwen3.
Figure 2: Overview of AF1. Null-space-Aware Binary Factorization (NABF) constructs Hessian-aware surrogate weights, suppresses SVID projection errors, and performs scale-only reconstruction. Hierarchical Shapley Allocation (HiSA) allocates structural budgets from coarse layer-level capacity to fine-grained module-level dimensions.
Method
#Bits (W)
LLaMA-3-8B
LLaMA-3-70B
Qwen3-8B
Qwen3-14B
Qwen3-32B
Gemma-3-4B-it
Gemma-3-12B-it
0-shot 7
Wiki
0-shot 7
Wiki
0-shot 7
Wiki
0-shot 7
Wiki
0-shot 7
Wiki
0-shot 7
Wiki
0-shot 7
Wiki
Avg.( ↑ )
( ↓ )
Avg.( ↑ )
( ↓ )
Avg.( ↑ )
( ↓ )
Avg.( ↑ )
( ↓ )
Avg.( ↑ )
( ↓ )
Avg.( ↑ )
( ↓ )
Avg.( ↑ )
( ↓ )
BF16
16
72.51
6.14
79.08
2.86
69.09
9.00
72.47
8.64
72.42
7.61
67.12
17.39
72.20
25.20
RTN
1.00
25.82
2.57e6
24.88
3.77e4
25.28
7.81e6
25.55
1.37e8
25.41
3.82e6
25.28
2.12e7
25.30
7.29e7
BiLLM
2.88
35.38
48.18
28.32
137.64
33.70
96.21
53.53
28.66
61.23
16.79
32.33
134.42
38.41
381.19
STBLLM (4:8)
3.50
29.43
196.03
26.55
963.92
28.02
291.76
40.88
48.80
55.86
17.31
29.31
202.54
31.46
4.69e5
Table 1: Comparison of perplexity on WikiText2 and averaged accuracy on seven zero-shot tasks. Bold and underline denote the best and second-best quantized results. Full results are in Appendix A.4.1 .
Model
Method
#Bits(W)
Model Size
MMLU-Pro
HumanEval
GSM8K
LLaMA-3.1 -8B-Instruct
BF16
16
16.07GB
46.64
67.07
83.24
BiLLM
2.88
3.75GB
8.77
15.33
21.36
STBLLM (4:8)
3.50
4.32GB
13.74
10.15
10.83
ARB-LLM RC
2.51
3.36GB
10.16
20.12
30.38
HBLLM row
3.25
4.15GB
23.57
28.97
40.26
AF1
1.00
1.56GB
20.12
36.71
44.78
Table 2: Results on instruction-tuned models across three challenging benchmarks. Bold and underline denote the best and second-best quantized results.
Figure 3: Hyperparameter sensitivity of HiSA on WikiText2 perplexity. (a) Layer-level coarse-grained allocation under different τ and Mlayer . (b) Block-level fine-grained allocation under different α and Mblock .
Model
NABF
HiSA
Wiki2
0-shot 7
Step1
Step2
Step3
Layer
Module
PPL ( ↓ )
Avg. ( ↑ )
LLaMA- 3.2-3B
✗
✗
✗
✗
8.9e2
25.48
✓
✗
✗
1.3e2
29.31
✓
✓
✗
41.34
34.85
✓
✓
✓
30.47
40.79
✓
✓
✗
25.52
42.30
Table 3: Combined ablation on LLaMA-3.2-3B. Step1–3 denote surrogate reparameterization, null-space binary factorization, and scale-only reconstruction; Layer and Module denote the two stages of HiSA allocation.
Figure 4: Quantization time and WikiText2 perplexity comparison under near-1-bit compression.
Figure 5: Inference memory and decoding throughput comparison across BF16, GPTQ-W4, and AF1.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Model
Method
#Bits(W)
AE ↑
AC ↑
HS ↑
LO ↑
LS ↑
PQ ↑
WG ↑
Avg. 7 ↑
LLaMA-3-8B
BF16
16
77.90
52.82
79.07
75.63
68.58
80.63
72.93
72.51
RTN
1.00
24.71
25.94
26.63
0.00
0.00
51.85
51.62
25.82
BiLLM
2.88
36.78
22.18
34.81
28.76
13.00
58.49
53.67
35.38
STBLLM (4:8)
3.50
31.10
21.76
31.29
11.84
5.88
54.52
49.64
29.43
ARB-LLM RC
2.51
48.78
28.33
43.55
50.65
29.83
65.61
56.75
46.21
HBLLM row
3.25
54.12
32.68
60.22
58.51
46.40
70.35
65.19
55.35
Appendix
Table 4: Detailed zero-shot accuracy on ARC-Easy (AE), ARC-Challenge (AC), HellaSwag (HS), LAMBADA-openai (LO), LAMBADA-standard (LS), PIQA (PQ), and WinoGrande (WG). The average score is computed over the seven zero-shot tasks. Bold and underline denote the best and second-best quantized results within each model.
η
LLaMA-3-8B
Qwen3-14B
Gemma-3-4B-it
Avg.
0.01
22.18
13.32
32.82
22.77
0.02
22.35
13.45
32.74
22.85
0.03
22.51
13.58
33.02
23.04
0.04
22.43
13.72
33.11
23.09
0.05
22.69
13.66
33.23
23.19
0.06
22.58
13.84
33.34
23.25
Appendix
Table 5: Ablation on the residual-energy threshold η used in the adaptive null-space cutoff. Results are reported as WikiText2 perplexity on LLaMA-3-8B, Qwen3-14B, and Gemma-3-4B-it. Bold and underline denote the best and second-best results, respectively.
Model
Avg. Bits(W)
General Allocation Baselines (PPL ↓ )
HiSA Variants (PPL ↓ )
Uniform
LIM
ZD
Act.
NLL
Only Dir.
Only Mag.
HiSA
LLaMA-3-8B
1.00
35.84
29.67
32.51
27.94
25.86
24.59
23.33
22.18
Qwen3-8B
1.00
28.92
23.38
25.71
21.45
19.37
18.15
17.59
16.26
Appendix
Table 6: Ablation on different allocation-sensitivity metrics and HiSA variants under the same 1.00-bit weight budget. We report WikiText2 perplexity (PPL; lower is better). Only Dir. and Only Mag. use only directional and magnitude distortion, respectively, while HiSA uses the full Soft-OR fusion of both distortion modes. Bold denotes the best result.
Figure 6: Additional hyperparameter sensitivity of HiSA on LLaMA-3-8B . We report WikiText2 perplexity under different values of the layer-level temperature coefficient τ , the layer-level sampling number Mlayer , the block-level smoothing exponent α , and the block-level sampling number Mblock .
Figure 7: Additional hyperparameter sensitivity of HiSA on Gemma-3-4B-it . We report WikiText2 perplexity under different values of the layer-level temperature coefficient τ , the layer-level sampling number Mlayer , the block-level smoothing exponent α , and the block-level sampling number Mblock .
Figure 8: Ablation on calibration data. We use C4 as the calibration corpus and report WikiText2 perplexity after quantization. (a) varying the number of calibration samples. (b) varying the random seed for calibration-data sampling.
Prompt
Method
Response
Assessment
Q1: I have 3 apples, buy 5 more, and give away 2. How many apples are left? Answer: 6
BF16
You start with 3 apples, buy 5 more, and give away 2. Final answer: 6 apples .
Correct
BiLLM
The ** ** ** ** ** ** ** ** ** ** ⋯
Degenerated
ARB-LLM
3+5=8 , and 8−2=6 . 6 apples are left.
Correct
HBLLM
3+5=8 apples, then 8−2=6 apples.
Correct
AF1
You start with 3 apples, buy 5 more, making 8 apples. Then you give away 2, so you have 6 apples left.
Correct
Q2: What are the capitals of Canada, Japan, and Germany? Answer: Ottawa, Tokyo, Berlin
BF16
Canada: Ottawa ; Japan: Tokyo ; Germany: Berlin .
Correct
Appendix
Table 7: Qualitative examples on Qwen3-14B-Instruct under full precision and different binary PTQ methods. All prompts have objective answers. Dark green marks correct key information, dark red marks wrong answers or degenerated repetitions, and dark orange indicates partially correct but unstable generations. Repeated continuations are abbreviated for readability.
Large language models (LLMs) have driven major progress in NLP, yet their substantial memory and compute demands still hinder practical deployment. Binarization can compress weights to 1 bit, fundamentally lowering compute and bandwidth cost. However, existing methods cannot address activation heavy tails and thus must keep activations in high precision, preventing true end-to-end acceleration. To overcome this limitation, we propose BWLA (Binarized Weights and Low-bit Activations), the first post-training quantization framework that preserves high accuracy while achieving 1-bit weight quantization together with low-bit activations (e.g., 6 bits). The Orthogonal-Kronecker Transformation (OKT) learns an orthogonal mapping via EM minimization, converting unimodal weights into symmetric bimodal forms while suppressing activation tails and incoherence. The Proximal SVD Projection (PSP) then performs lightweight low-rank refinement through proximal SVD projection, further enhancing quantizability with minimal overhead. On Qwen3-32B, BWLA reaches a Wikitext2 perplexity of 11.92 under 6-bit activations (vs. 38 from SOTA), improves five zero-shot tasks by more than 70%, and delivers 3.26 times inference speedup, demonstrating strong potential for real-world LLM compression and acceleration.
Deploying large language models (LLMs) in resource-constrained environments is hindered by heavy computational and memory requirements. We present LBLLM, a lightweight binarization framework that achieves effective W(1+1)A4 quantization through a novel three-stage quantization strategy. The framework proceeds as follows: (1) initialize a high-quality quantized model via PTQ; (2) quantize binarized weights, group-wise bitmaps, and quantization parameters through layer-wise distillation while keeping activations in full precision; and (3) training learnable activation quantization factors to dynamically quantize activations to 4 bits. This decoupled design mitigates interference between weight and activation quantization, yielding greater training stability and better inference accuracy. LBLLM, trained only using 0.016B tokens with a single GPU, surpasses existing state-of-the-art binarization methods on W2A4 quantization settings across tasks of language modeling, commonsense QA, and language understanding. These results demonstrate that extreme low-bit quantization of LLMs can be both practical and highly effective without introducing any extra high-precision channels or rotational matrices commonly used in recent PTQ-based works, offering a promising path toward efficient LLM deployment in resource-limited situations.
Siqing Song, Chuang Wang, Yong Lang +2
MAIS, Institute of Automation, Chinese Academy of Sciences, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, China · Central Media Technology Institute, Huawei
Deploying large language models (LLMs) is challenging due to their massive parameters and high computational costs. Ultra low-bit quantization can significantly reduce storage and accelerate inference, but extreme compression (i.e., mean bit-width <= 2) often leads to severe performance degradation. To address this, we propose Squeeze10-LLM, effectively "squeezing" 16-bit LLMs' weights by 10 times. Specifically, Squeeze10-LLM is a staged mixed-precision post-training quantization (PTQ) framework and achieves an average of 1.6 bits per weight by quantizing 80% of the weights to 1 bit and 20% to 4 bits. We introduce Squeeze10LLM with two key innovations: Post-Binarization Activation Robustness (PBAR) and Full Information Activation Supervision (FIAS). PBAR is a refined weight significance metric that accounts for the impact of quantization on activations, improving accuracy in low-bit settings. FIAS is a strategy that preserves full activation information during quantization to mitigate cumulative error propagation across layers. Experiments on LLaMA and LLaMA2 show that Squeeze10-LLM achieves state-of-the-art performance for sub-2bit weight-only quantization, improving average accuracy from 43% to 56% on six zero-shot classification tasks--a significant boost over existing PTQ methods.
Qingcheng Zhu, Yangyang Ren, Linlin Yang +6
Beihang University · Communication University of China · Beijing Jiaotong University