# Transformers to SSMs: Distilling Quadratic Knowledge to Subquadratic Models

arXiv: https://arxiv.org/abs/2408.10189 · HTML: https://mlsanity.com/paper/2408.10189/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Placed in Core SSM architectures for language, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 42 of its 55 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Ring Attention with Blockwise Transformers for Near-Infinite Context](https://mlsanity.com/paper/2310.01889/) (2023)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [MambaVision: A Hybrid Mamba-Transformer Vision Backbone](https://mlsanity.com/paper/2407.08083/) (2024)
- [Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling](https://mlsanity.com/paper/2406.07522/) (2024)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)
- [Understanding Knowledge Distillation in Non-autoregressive Machine Translation](https://mlsanity.com/paper/1911.02727/) (2019)
- [The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry](https://mlsanity.com/paper/2402.04347/) (2024)
- [Selective Structured State-Spaces for Long-Form Video Understanding](https://mlsanity.com/paper/2303.14526/) (2023)

## Built on by (most cited first, 30 of 67)

- [MoBA: Mixture of Block Attention for Long-Context LLMs](https://mlsanity.com/paper/2502.13189/) (2025)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [The Mamba in the Llama: Distilling and Accelerating Hybrid Models](https://mlsanity.com/paper/2408.15237/) (2024)
- [Gated Slot Attention for Efficient Linear-Time Sequence Modeling](https://mlsanity.com/paper/2409.07146/) (2024)
- [Dynamic Chunking for End-to-End Hierarchical Sequence Modeling](https://mlsanity.com/paper/2507.07955/) (2025)
- [End-to-End Test-Time Training for Long Context](https://mlsanity.com/paper/2512.23675/) (2025)
- [Jet-Nemotron: Efficient Language Model with Post Neural Architecture Search](https://mlsanity.com/paper/2508.15884/) (2025)
- [Llamba: Scaling Distilled Recurrent Models for Efficient Language Processing](https://mlsanity.com/paper/2502.14458/) (2025)
- [Liger: Linearizing Large Language Models to Gated Recurrent Structures](https://mlsanity.com/paper/2503.01496/) (2025)
- [RADLADS: Rapid Attention Distillation to Linear Attention Decoders at Scale](https://mlsanity.com/paper/2505.03005/) (2025)
- [Thinking Slow, Fast: Scaling Inference Compute with Distilled Reasoners](https://mlsanity.com/paper/2502.20339/) (2025)
- [M1: Towards Scalable Test-Time Compute with Mamba Reasoning Models](https://mlsanity.com/paper/2504.10449/) (2025)
- [R-Sparse: Rank-Aware Activation Sparsity for Efficient LLM Inference](https://mlsanity.com/paper/2504.19449/) (2025)
- [Zebra-Llama: Towards Extremely Efficient Hybrid Models](https://mlsanity.com/paper/2505.17272/) (2025)
- [Hybrid Linear Attention Done Right: Efficient Distillation and Effective Architectures for Extremely Long Contexts](https://mlsanity.com/paper/2601.22156/) (2026)
- [Understanding the Skill Gap in Recurrent Language Models: The Role of the Gather-and-Aggregate Mechanism](https://mlsanity.com/paper/2504.18574/) (2025)
- [Comba: Improving Bilinear RNNs with Closed-loop Control](https://mlsanity.com/paper/2506.02475/) (2025)
- [Hybrid Architectures for Language Models: Systematic Analysis and Design Insights](https://mlsanity.com/paper/2510.04800/) (2025)
- [LightTransfer: Your Long-Context LLM is Secretly a Hybrid Model with Effortless Adaptation](https://mlsanity.com/paper/2410.13846/) (2024)
- [Multimodal Mamba: Decoder-only Multimodal State Space Model via Quadratic to Linear Distillation](https://mlsanity.com/paper/2502.13145/) (2025)
- [LoLA: Low-Rank Linear Attention With Sparse Caching](https://mlsanity.com/paper/2505.23666/) (2025)
- [Exploring Diffusion Transformer Designs via Grafting](https://mlsanity.com/paper/2506.05340/) (2025)
- [Autocorrelation Matters: Understanding the Role of Initialization Schemes for State Space Models](https://mlsanity.com/paper/2411.19455/) (2024)
- [Advancing Intelligent Sequence Modeling: Evolution, Trade-offs, and Applications of State-Space Architectures from S4 to Mamba](https://mlsanity.com/paper/2503.18970/) (2025)
- [Bolmo: Byteifying the Next Generation of Language Models](https://mlsanity.com/paper/2512.15586/) (2025)
- [RAD: Redundancy-Aware Distillation for Hybrid Models via Self-Speculative Decoding](https://mlsanity.com/paper/2505.22135/) (2025)
- [TransMamba: Fast Universal Architecture Adaption from Transformers to Mamba](https://mlsanity.com/paper/2502.15130/) (2025)
- [LaTIM: Measuring Latent Token-to-Token Interactions in Mamba Models](https://mlsanity.com/paper/2502.15612/) (2025)
- [On Pruning State-Space LLMs](https://mlsanity.com/paper/2502.18886/) (2025)
- [MaTVLM: Hybrid Mamba-Transformer for Efficient Vision-Language Modeling](https://mlsanity.com/paper/2503.13440/) (2025)

## Abstract (arXiv)

Transformer architectures have become a dominant paradigm for domains like language modeling but suffer in many inference settings due to their quadratic-time self-attention. Recently proposed subquadratic architectures, such as Mamba, have shown promise, but have been pretrained with substantially less computational resources than the strongest Transformer models. In this work, we present a method that is able to distill a pretrained Transformer architecture into alternative architectures such as state space models (SSMs). The key idea to our approach is that we can view both Transformers and SSMs as applying different forms of mixing matrices over the token sequences. We can thus progressively distill the Transformer architecture by matching different degrees of granularity in the SSM: first matching the mixing matrices themselves, then the hidden units at each block, and finally the end-to-end predictions. Our method, called MOHAWK, is able to distill a Mamba-2 variant based on the Phi-1.5 architecture (Phi-Mamba) using only 3B tokens and a hybrid version (Hybrid Phi-Mamba) using 5B tokens. Despite using less than 1% of the training data typically used to train models from scratch, Phi-Mamba boasts substantially stronger performance compared to all past open-source non-Transformer models. MOHAWK allows models like SSMs to leverage computational resources invested in training Transformer-based architectures, highlighting a new avenue for building such models.