# LoLCATs: On Low-Rank Linearizing of Large Language Models

arXiv: https://arxiv.org/abs/2410.10254 · HTML: https://mlsanity.com/paper/2410.10254/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 67 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 30 of 55)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [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)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)

## Built on by (most cited first, 27 of 27)

- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [ThunderKittens: Simple, Fast, and Adorable AI Kernels](https://mlsanity.com/paper/2410.20399/) (2024)
- [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)
- [Towards AI Search Paradigm](https://mlsanity.com/paper/2506.17188/) (2025)
- [Hybrid Linear Attention Done Right: Efficient Distillation and Effective Architectures for Extremely Long Contexts](https://mlsanity.com/paper/2601.22156/) (2026)
- [Multimodal Mamba: Decoder-only Multimodal State Space Model via Quadratic to Linear Distillation](https://mlsanity.com/paper/2502.13145/) (2025)
- [Distributed LLMs and Multimodal Large Language Models: A Survey on Advances, Challenges, and Future Directions](https://mlsanity.com/paper/2503.16585/) (2025)
- [KVLinC : KV Cache Quantization with Hadamard Rotation and Linear Correction](https://mlsanity.com/paper/2510.05373/) (2025)
- [ViT-Linearizer: Distilling Quadratic Knowledge into Linear-Time Vision Models](https://mlsanity.com/paper/2504.00037/) (2025)
- [ViT-AdaLA: Adapting Vision Transformers with Linear Attention](https://mlsanity.com/paper/2603.16063/) (2026)
- [On-the-Fly Adaptive Distillation of Transformer to Dual-State Linear Attention](https://mlsanity.com/paper/2506.09316/) (2025)
- [SPLA: Block Sparse Plus Linear Attention for Long Context Modeling](https://mlsanity.com/paper/2601.22379/) (2026)
- [Neural Attention Search Linear: Towards Adaptive Token-Level Hybrid Attention Models](https://mlsanity.com/paper/2602.03681/) (2026)
- [Linearizing Vision Transformer with Test-Time Training](https://mlsanity.com/paper/2605.02772/) (2026)
- [Untangling Component Imbalance in Hybrid Linear Attention Conversion Methods](https://mlsanity.com/paper/2510.05901/) (2025)
- [Taylor-Calibrate: Principled Initialization for Hybrid Linear Attention Distillation](https://mlsanity.com/paper/2606.16429/) (2026)
- [Language Modeling With Factorization Memory](https://mlsanity.com/paper/2511.00315/) (2025)
- [Network of Theseus (like the ship)](https://mlsanity.com/paper/2512.04198/) (2025)
- [GLIDE: Guided Layerwise Hybrid Attention for Efficient LLM Inference](https://mlsanity.com/paper/2607.24788/) (2026)
- [Retrofitting Linear Attention into Diffusion Language Models](https://mlsanity.com/paper/2608.06628/) (2026)
- [Switching Linear Attention](https://mlsanity.com/paper/2609.39034/) (2026)
- [The Evolution of Attention in Large Language Models: Mechanisms, Trade-offs, and Emerging Trends](https://mlsanity.com/paper/2609.39661/) (2026)
- [Robust Parameter-Efficient LLM Adaptation on Analog Hardware](https://mlsanity.com/paper/2610.05318/) (2026)
- [Bridging KV-Cache Quantization and Linear Attention: From Theory to Pretrained Weight Migration](https://mlsanity.com/paper/2610.11214/) (2026)

## Abstract (arXiv)

Recent works show we can linearize large language models (LLMs) -- swapping the quadratic attentions of popular Transformer-based LLMs with subquadratic analogs, such as linear attention -- avoiding the expensive pretraining costs. However, linearizing LLMs often significantly degrades model quality, still requires training over billions of tokens, and remains limited to smaller 1.3B to 7B LLMs. We thus propose Low-rank Linear Conversion via Attention Transfer (LoLCATs), a simple two-step method that improves LLM linearizing quality with orders of magnitudes less memory and compute. We base these steps on two findings. First, we can replace an LLM's softmax attentions with closely-approximating linear attentions, simply by training the linear attentions to match their softmax counterparts with an output MSE loss ("attention transfer"). Then, this enables adjusting for approximation errors and recovering LLM quality simply with low-rank adaptation (LoRA). LoLCATs significantly improves linearizing quality, training efficiency, and scalability. We significantly reduce the linearizing quality gap and produce state-of-the-art subquadratic LLMs from Llama 3 8B and Mistral 7B v0.1, leading to 20+ points of improvement on 5-shot MMLU. Furthermore, LoLCATs does so with only 0.2% of past methods' model parameters and 0.4% of their training tokens. Finally, we apply LoLCATs to create the first linearized 70B and 405B LLMs (50x larger than prior work). When compared with prior approaches under the same compute budgets, LoLCATs significantly improves linearizing quality, closing the gap between linearized and original Llama 3.1 70B and 405B LLMs by 77.8% and 78.1% on 5-shot MMLU.