# MatGPTQ: Efficient and Accurate Inference over Nested Quantized Models

arXiv: https://arxiv.org/abs/2602.03537 · HTML: https://mlsanity.com/paper/2602.03537/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 30 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [AMC: AutoML for Model Compression and Acceleration on Mobile Devices](https://mlsanity.com/paper/1802.03494/) (2018)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Outlier Weighed Layerwise Sparsity (OWL): A Missing Secret Sauce for Pruning LLMs to High Sparsity](https://mlsanity.com/paper/2310.05175/) (2023)
- [8-Bit Approximations for Parallelism in Deep Learning](https://mlsanity.com/paper/1511.04561/) (2015)
- [Any-Precision LLM: Low-Cost Deployment of Multiple, Different-Sized LLMs](https://mlsanity.com/paper/2402.10517/) (2024)
- [MARLIN: Mixed-Precision Auto-Regressive Parallel Inference on Large Language Models](https://mlsanity.com/paper/2408.11743/) (2024)
- [SPDY: Accurate Pruning with Speedup Guarantees](https://mlsanity.com/paper/2201.13096/) (2022)
- ["Give Me BF16 or Give Me Death"? Accuracy-Performance Trade-Offs in LLM Quantization](https://mlsanity.com/paper/2411.02355/) (2024)
- [Who Says Elephants Can't Run: Bringing Large Scale MoE Models into Cloud Scale Production](https://mlsanity.com/paper/2211.10017/) (2022)
- [D2MoE: Dual Routing and Dynamic Scheduling for Efficient On-Device MoE-based LLM Serving](https://mlsanity.com/paper/2504.15299/) (2025)
- [Progressive Mixed-Precision Decoding for Efficient LLM Inference](https://mlsanity.com/paper/2410.13461/) (2024)
- [Matryoshka Quantization](https://mlsanity.com/paper/2502.06786/) (2025)
- [AnyBCQ: Hardware Efficient Flexible Binary-Coded Quantization for Multi-Precision LLMs](https://mlsanity.com/paper/2510.10467/) (2025)
- [NestQuant: Post-Training Integer-Nesting Quantization for On-Device DNN](https://mlsanity.com/paper/2506.17870/) (2025)
- [TruncQuant: Truncation-Ready Quantization for DNNs with Flexible Weight Bit Precision](https://mlsanity.com/paper/2506.11431/) (2025)

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

- [Recurrent Residual Quantization: A Progressive Multi-Precision Representation for LLMs](https://mlsanity.com/paper/2608.04048/) (2026)
- [In-Cell Learning: Language Models That Update Their Own Weights in Sequence Without Changing the File They Ship](https://mlsanity.com/paper/2608.20873/) (2026)
- [DPS: Dual-Mode Precision LLM Serving with Semi-Unified Memory](https://mlsanity.com/paper/2609.34380/) (2026)

## Abstract (arXiv)

Matryoshka Quantization (MatQuant), Any-Precision-LLM (AP) and AnyBCQ (AB) are recent quantization approaches showing that a single integer-quantized model can be served across multiple precisions. In this paradigm, lower-precision models are extracted from a higher-precision model by simply reading fewer bits of the weights. This enables a single checkpoint to cover a wide range of memory and latency budgets, but makes both quantization and efficient execution substantially harder. Existing methods rely on expensive quantization-aware training (QAT) or gradient-based post-training quantization (PTQ) rather than fast one-shot PTQ, and offer limited system support: dedicated kernels are either missing or restricted to single- or small-batch decoding. We address these limitations with Post-Training Matryoshka Quantization (MatGPTQ), an end-to-end pipeline for nested-model quantization and inference. MatGPTQ casts Matryoshka quantization as multi-precision error compensation, producing a single "sliceable" parent model jointly optimized for multiple target precisions in one pass over a small calibration set. We further refine the MatQuant representation so that an r-bit model reads exactly r bits, and introduce the first dedicated inference kernels for this format, supporting batch sizes beyond one and integrated into vLLM. Across standard LLMs and benchmarks, MatGPTQ outperforms MatQuant while remaining competitive with AP and AB at the smallest checkpoint size, and our kernels achieve end-to-end speedups of up to 3.5× over BF16 at the low-bit regime. Overall, MatGPTQ makes nested quantized models practical to serve from a single, compact checkpoint. Code is available at https://github.com/IST-DASLab/MatGPTQ.