# QET: Enhancing Quantized LLM Parameters and KV cache Compression through Element Substitution and Residual Clustering

arXiv: https://arxiv.org/abs/2407.03637 · HTML: https://mlsanity.com/paper/2407.03637/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache quantization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 22 of its 32 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Placed in

- Efficient LLM inference and serving / [KV cache quantization](https://mlsanity.com/inference/kv-cache-quantization/)

## Builds on (most cited first, 22 of 22)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [Release Strategies and the Social Impacts of Language Models](https://mlsanity.com/paper/1908.09203/) (2019)
- [Scissorhands: Exploiting the Persistence of Importance Hypothesis for LLM KV Cache Compression at Test Time](https://mlsanity.com/paper/2305.17118/) (2023)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [InfiniGen: Efficient Generative Inference of Large Language Models with Dynamic KV Cache Management](https://mlsanity.com/paper/2406.19707/) (2024)
- [Keyformer: KV Cache Reduction through Key Tokens Selection for Efficient Generative Inference](https://mlsanity.com/paper/2403.09054/) (2024)
- [WKVQuant: Quantizing Weight and Key/Value Cache for Large Language Models Gains More](https://mlsanity.com/paper/2402.12065/) (2024)
- [SKVQ: Sliding-window Key and Value Cache Quantization for Large Language Models](https://mlsanity.com/paper/2405.06219/) (2024)
- [MLKV: Multi-Layer Key-Value Heads for Memory Efficient Transformer Decoding](https://mlsanity.com/paper/2406.09297/) (2024)
- [Online Product Quantization](https://mlsanity.com/paper/1711.10775/) (2017)
- [Scalable Image Retrieval by Sparse Product Quantization](https://mlsanity.com/paper/1603.04614/) (2016)

## Abstract (arXiv)

The matrix quantization entails representing matrix elements in a more space-efficient form to reduce storage usage, with dequantization restoring the original matrix for use. We formulate the Quantization Error Minimization (QEM) problem as minimizing the distance between a matrix before and after quantization, under the condition that the quantized matrix occupies the same memory space. Matrix quantization is crucial in various applications, including Large Language Models (LLMs) weight quantization, vector databases, KV cache quantization, graph compression, and image compression. Recent advancements in LLMs, such as GPT-4 and BERT, have highlighted the importance of matrix compression due to the large size of parameters and KV cache, which are stored as matrices. We propose Quantum Entanglement Trees (QET) to address the QEM problem by leveraging the local orderliness of matrix elements, involving iterative element swapping to form a locally ordered matrix. This matrix is then grouped and quantized by columns. To enhance QET, we introduce two optimizations: further quantizing residuals to reduce MSE, and using masking and batch processing to accelerate the algorithm. Experimental results demonstrate that QET can effectively reduce MSE to 5.05%, 13.33%, and 11.89% of the current best method on the LLM dataset, K cache, and V cache, respectively. Our contributions include the abstraction of the QEM problem, the design of the QET algorithm, and the proposal of two optimizations to improve accuracy and speed.