# More Than Bits: Multi-Envelope Double Binary Factorization for Extreme Quantization

arXiv: https://arxiv.org/abs/2512.24545 · HTML: https://mlsanity.com/paper/2512.24545/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [QTIP: Quantization with Trellises and Incoherence Processing](https://mlsanity.com/paper/2406.11235/) (2024)
- [PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compression](https://mlsanity.com/paper/2405.14852/) (2024)
- [Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization](https://mlsanity.com/paper/2504.09629/) (2025)
- [STBLLM: Breaking the 1-Bit Barrier with Structured Binary LLMs](https://mlsanity.com/paper/2408.01803/) (2024)
- [Controlling Continuous Relaxation for Combinatorial Optimization](https://mlsanity.com/paper/2309.16965/) (2023)
- [LittleBit: Ultra Low-Bit Quantization via Latent Factorization](https://mlsanity.com/paper/2506.13771/) (2025)
- [Learning Quantized Neural Nets by Coarse Gradient Method for Non-linear Classification](https://mlsanity.com/paper/2011.11256/) (2020)
- [Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling](https://mlsanity.com/paper/2409.02135/) (2024)
- [LPCD: Unified Framework from Layer-Wise to Submodule Quantization](https://mlsanity.com/paper/2512.01546/) (2025)
- [High-Dimensional Learning Dynamics of Quantized Models with Straight-Through Estimator](https://mlsanity.com/paper/2510.10693/) (2025)

## Built on by (most cited first, 3 of 3)

- [OneComp: One-Line Revolution for Generative AI Model Compression](https://mlsanity.com/paper/2603.28845/) (2026)
- [Signs Beat Floats: Low-Rank Double-Binary Adaptation for On-Device Fine-Tuning](https://mlsanity.com/paper/2605.24058/) (2026)
- [From Sweep to Seam: Interleaved Cross-Block Post-Training Quantization](https://mlsanity.com/paper/2608.09595/) (2026)

## Abstract (arXiv)

For extreme low-bit quantization of large language models (LLMs), Double Binary Factorization (DBF) is attractive as it enables efficient inference without sacrificing accuracy. However, the scaling parameters of DBF are too restrictive; after factoring out signs, all rank components share the same magnitude profile, resulting in performance saturation. We propose Multi-envelope DBF (MDBF), which retains a shared pair of 1-bit sign bases but replaces the single envelope with a rank-l envelope. By sharing sign matrices among envelope components, MDBF effectively maintains a binary carrier and utilizes the limited memory budget for magnitude expressiveness. We also introduce a closed-form initialization and an alternating refinement method to optimize MDBF. Across the LLaMA and Qwen families, MDBF enhances perplexity and zero-shot accuracy over previous binary formats at matched bits per weight while preserving the same deployment-friendly inference primitive.