# Matryoshka Quantization

arXiv: https://arxiv.org/abs/2502.06786 · HTML: https://mlsanity.com/paper/2502.06786/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 39 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [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)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [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)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [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)
- [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)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks](https://mlsanity.com/paper/1506.05751/) (2015)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [MatFormer: Nested Transformer for Elastic Inference](https://mlsanity.com/paper/2310.07707/) (2023)
- [Learning Ordered Representations with Nested Dropout](https://mlsanity.com/paper/1402.0915/) (2014)
- [BitDistiller: Unleashing the Potential of Sub-4-Bit LLMs via Self-Distillation](https://mlsanity.com/paper/2402.10631/) (2024)
- [AffineQuant: Affine Transformation Quantization for Large Language Models](https://mlsanity.com/paper/2403.12544/) (2024)
- [Any-Precision Deep Neural Networks](https://mlsanity.com/paper/1911.07346/) (2019)

## Built on by (most cited first, 14 of 14)

- [Adaptive Audio-Visual Speech Recognition via Matryoshka-Based Multimodal LLMs](https://mlsanity.com/paper/2503.06362/) (2025)
- [AnyBCQ: Hardware Efficient Flexible Binary-Coded Quantization for Multi-Precision LLMs](https://mlsanity.com/paper/2510.10467/) (2025)
- [DP-LLM: Runtime Model Adaptation with Dynamic Layer-wise Precision Assignment](https://mlsanity.com/paper/2508.06041/) (2025)
- [Efficient Multi-bit Quantization Network Training via Weight Bias Correction and Bit-wise Coreset Sampling](https://mlsanity.com/paper/2510.20673/) (2025)
- [MatGPTQ: Efficient and Accurate Inference over Nested Quantized Models](https://mlsanity.com/paper/2602.03537/) (2026)
- [WinQ: Accelerating Quantization-Aware Training of Language Models Around Saddle Points](https://mlsanity.com/paper/2605.17471/) (2026)
- [Recurrent Residual Quantization: A Progressive Multi-Precision Representation for LLMs](https://mlsanity.com/paper/2608.04048/) (2026)
- [MoBiQuant: Mixture-of-Bits Quantization for Token-Adaptive Any-Precision LLM](https://mlsanity.com/paper/2602.20191/) (2026)
- [Multi-Bitwidth Quantization for LLMs Using Additive Codebooks](https://mlsanity.com/paper/2606.12876/) (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)
- [ELMoE-3D: Leveraging Intrinsic Elasticity of MoE for Hybrid-Bonding-Enabled Self-Speculative Decoding in On-Premises Serving](https://mlsanity.com/paper/2604.14626/) (2026)
- [BitNet Text Embeddings](https://mlsanity.com/paper/2606.25674/) (2026)
- [MRVQ: One Resident Index for Dimension- and Rate-Elastic Vector Search](https://mlsanity.com/paper/2610.03651/) (2026)
- [DuoRate: Two-Rate Per-Expert Precision Allocation for Mixture-of-Experts Serving](https://mlsanity.com/paper/2610.13328/) (2026)

## Abstract (arXiv)

Quantizing model weights is critical for reducing the communication and inference costs of large models. However, quantizing models -- especially to low precisions like int4 or int2 -- requires a trade-off in model quality; int2, in particular, is known to severely degrade model quality. Consequently, practitioners are often forced to maintain multiple models with different quantization levels or serve a single model that best satisfies the quality-latency trade-off. On the other hand, integer data types, such as int8, inherently possess a nested (Matryoshka) structure where smaller bit-width integers, like int4 or int2, are nested within the most significant bits. Leveraging this insight, in this paper, we propose Matryoshka Quantization (MatQuant), a novel multi-scale quantization technique that alleviates the aforementioned challenge. This technique allows us to train and maintain a single quantized model but serve it with the precision demanded by the deployment. Furthermore, leveraging MatQuant's co-training and co-distillation regularization, int2 precision models extracted by MatQuant outperform standard int2 quantization by up to to 4% and 7% with OmniQuant and QAT as base algorithms respectively. Finally, we demonstrate that by using an extra bit to represent outliers, a model with an effective precision of 2.05-bit gives an additional 6% improvement with OmniQuant as the base algorithm.