# CodeGEMM: A Codebook-Centric Approach to Efficient GEMM in Quantized LLMs

arXiv: https://arxiv.org/abs/2512.17970 · HTML: https://mlsanity.com/paper/2512.17970/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 30 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [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)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (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)
- [GPTVQ: The Blessing of Dimensionality for LLM Quantization](https://mlsanity.com/paper/2402.15319/) (2024)
- [LLM Pruning and Distillation in Practice: The Minitron Approach](https://mlsanity.com/paper/2408.11796/) (2024)
- [PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compression](https://mlsanity.com/paper/2405.14852/) (2024)
- [VPTQ: Extreme Low-bit Vector Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2409.17066/) (2024)
- [T-MAC: CPU Renaissance via Table Lookup for Low-Bit LLM Deployment on Edge](https://mlsanity.com/paper/2407.00088/) (2024)
- [FlexRound: Learnable Rounding based on Element-wise Division for Post-Training Quantization](https://mlsanity.com/paper/2306.00317/) (2023)
- [ShiftAddLLM: Accelerating Pretrained LLMs via Post-Training Multiplication-Less Reparameterization](https://mlsanity.com/paper/2406.05981/) (2024)
- [FineQuant: Unlocking Efficiency with Fine-Grained Weight-Only Quantization for LLMs](https://mlsanity.com/paper/2308.09723/) (2023)
- [FIGLUT: An Energy-Efficient Accelerator Design for FP-INT GEMM Using Look-Up Tables](https://mlsanity.com/paper/2503.06862/) (2025)
- [Look-Up mAI GeMM: Increasing AI GeMMs Performance by Nearly 2.5x via msGeMM](https://mlsanity.com/paper/2310.06178/) (2023)

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

- [EVA: Accelerating LLM Decoding via an Efficient Vector Quantization Architecture](https://mlsanity.com/paper/2605.24144/) (2026)
- [A Motion-Aware Vector Quantization Framework with Centroid Reuse for Efficient VLA Inference](https://mlsanity.com/paper/2607.24148/) (2026)
- [HBQ: Hierarchical Scaling Block Quantization with Hardware-Efficiency-Aware Design for Accurate LLM Inference](https://mlsanity.com/paper/2609.00450/) (2026)

## Abstract (arXiv)

Weight-only quantization is widely used to mitigate the memory-bound nature of LLM inference. Codebook-based methods extend this trend by achieving strong accuracy in the extremely low-bit regime (e.g., 2-bit). However, current kernels rely on dequantization, which repeatedly fetches centroids and reconstructs weights, incurring substantial latency and cache pressure. We present CodeGEMM, a codebook-centric GEMM kernel that replaces dequantization with precomputed inner products between centroids and activations stored in a lightweight Psumbook. At inference, code indices directly gather these partial sums, eliminating per-element lookups and reducing the on-chip footprint. The kernel supports the systematic exploration of latency-memory-accuracy trade-offs under a unified implementation. On Llama-3 models, CodeGEMM delivers 1.83x (8B) and 8.93x (70B) speedups in the 2-bit configuration compared to state-of-the-art codebook-based quantization at comparable accuracy and further improves computing efficiency and memory subsystem utilization.