# LPCD: Unified Framework from Layer-Wise to Submodule Quantization

arXiv: https://arxiv.org/abs/2512.01546 · HTML: https://mlsanity.com/paper/2512.01546/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [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)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [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)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [The case for 4-bit precision: k-bit Inference Scaling Laws](https://mlsanity.com/paper/2212.09720/) (2022)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (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)
- [QuantEase: Optimization-based Quantization for Language Models](https://mlsanity.com/paper/2309.01885/) (2023)
- [Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization](https://mlsanity.com/paper/2505.11695/) (2025)
- [LoaQ: Layer-wise Output Approximation Quantization](https://mlsanity.com/paper/2509.06297/) (2025)

## Built on by (most cited first, 6 of 6)

- [More Than Bits: Multi-Envelope Double Binary Factorization for Extreme Quantization](https://mlsanity.com/paper/2512.24545/) (2025)
- [A Guide to Large Language Models in Modeling and Simulation: From Core Techniques to Critical Challenges](https://mlsanity.com/paper/2602.05883/) (2026)
- [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)
- [SchurQuant: Groupwise Discrete Optimization for Layer-Wise LLM Quantization](https://mlsanity.com/paper/2608.15567/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) aims to preserve model-level behavior; however, most methods focus on individual linear layers. Even recent extensions, such as QEP and LoaQ, which mitigate error propagation or target specific submodules, still rely on layer-wise formulations and fail to capture the behavior of larger submodules. We introduce Layer-Projected Coordinate Descent (LPCD), a unified framework that extends PTQ beyond layers by optimizing relaxed objectives across arbitrary submodules and projecting the solutions with layer-wise quantizers. LPCD generalizes existing methods and provides a principled approach to quantizing complex submodules while maintaining the efficiency and compatibility of layer-wise PTQ pipelines. Across diverse LLM architectures and bit-widths, LPCD-based submodule quantization consistently enhances both layer-wise PTQ methods and existing submodule approaches.