# PTQTP: Post-Training Quantization to Trit-Planes for Large Language Models

arXiv: https://arxiv.org/abs/2509.16989 · HTML: https://mlsanity.com/paper/2509.16989/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 30 of 35)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [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)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (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)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [BiLLM: Pushing the Limit of Post-Training Quantization for LLMs](https://mlsanity.com/paper/2402.04291/) (2024)
- [LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Models](https://mlsanity.com/paper/2206.09557/) (2022)
- [QTIP: Quantization with Trellises and Incoherence Processing](https://mlsanity.com/paper/2406.11235/) (2024)
- [FlightLLM: Efficient Large Language Model Inference with a Complete Mapping Flow on FPGAs](https://mlsanity.com/paper/2401.03868/) (2024)

## Built on by (most cited first, 9 of 9)

- [GSQ: Highly-Accurate Low-Precision Scalar Quantization for LLMs via Gumbel-Softmax Sampling](https://mlsanity.com/paper/2604.18556/) (2026)
- [Sherry: Hardware-Efficient 1.25-Bit Ternary Quantization via Fine-grained Sparsification](https://mlsanity.com/paper/2601.07892/) (2026)
- [BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models](https://mlsanity.com/paper/2602.04163/) (2026)
- [Capability-Stratified Degradation in Ternary Language Models](https://mlsanity.com/paper/2608.28809/) (2026)
- [ExTernD: Expanded-Rank Ternary Decomposition Ternary LLM PTQ with Accuracy Approaching Any Quantization Level](https://mlsanity.com/paper/2607.13511/) (2026)
- [Tied Trit-Planes: Constraining PTQTP to a Uniform Nine-Level Quantizer, with a Persistent Folded Format for Disk-Streamed Mixture-of-Experts Serving](https://mlsanity.com/paper/2608.08910/) (2026)
- [FluxBin: Flexible LUT-based Ultra-low-bit LLM Inference by Algorithm-Kernel Synergy](https://mlsanity.com/paper/2608.15602/) (2026)
- [Post-Training Ternarization of Qwen3-4B Capability, Effective Bit Budget, Storage Compression, and Deployment](https://mlsanity.com/paper/2609.01962/) (2026)
- [Scaling Post-Training Ternarisation to Qwen3-8B Capability Retention, Reproduction, Lossless Packing, and Packed Execution](https://mlsanity.com/paper/2609.09240/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and representational capacity. While existing ultra-low-bit methods rely on binary approximations or quantization-aware training(QAT), they often suffer from either limited representational capacity or huge training resource overhead. We introduce PTQ to Trit-Planes (PTQTP), a structured PTQ framework that decomposes weight matrices into dual ternary -1, 0, 1 trit-planes. This approach achieves multiplication-free additive inference by decoupling weights into discrete topology (trit-planes) and continuous magnitude (scales), effectively enabling high-fidelity sparse approximation. PTQTP provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment without architectural modifications; and (3) uniform ternary operations that eliminate mixed-precision overhead. Comprehensive experiments on LLaMA3.x and Qwen3 (0.6B-70B) demonstrate that PTQTP significantly outperforms sub-4bit PTQ methods on both language reasoning tasks and mathematical reasoning as well as coding. PTQTP rivals the 1.58-bit QAT performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods, and the end-to-end inference speed achieves 4.63× faster than the FP16 baseline model, establishing a new and practical solution for efficient LLM deployment in resource-constrained environments. Code will available at https://github.com/HeXiao-55/PTQTP.