# The Devil in Linear Transformer

arXiv: https://arxiv.org/abs/2210.10340 · HTML: https://mlsanity.com/paper/2210.10340/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 36 references that are in the map.
- First posted on arXiv 19 Oct 2022.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [Sparse Sinkhorn Attention](https://mlsanity.com/paper/2002.11296/) (2020)
- [cosFormer: Rethinking Softmax in Attention](https://mlsanity.com/paper/2202.08791/) (2022)
- [Transformer Quality in Linear Time](https://mlsanity.com/paper/2202.10447/) (2022)
- [Audio-Visual Segmentation](https://mlsanity.com/paper/2207.05042/) (2022)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Long-Short Transformer: Efficient Transformers for Language and Vision](https://mlsanity.com/paper/2107.02192/) (2021)
- [Skyformer: Remodel Self-Attention with Gaussian Kernel and Nystr"om Method](https://mlsanity.com/paper/2111.00035/) (2021)
- [Implicit Motion Handling for Video Camouflaged Object Detection](https://mlsanity.com/paper/2203.07363/) (2022)
- [Sparse Attention with Linear Units](https://mlsanity.com/paper/2104.07012/) (2021)
- [Linear Complexity Randomized Self-attention Mechanism](https://mlsanity.com/paper/2204.04667/) (2022)
- [Vicinity Vision Transformer](https://mlsanity.com/paper/2206.10552/) (2022)
- [Neural Architecture Search on Efficient Transformers and Beyond](https://mlsanity.com/paper/2207.13955/) (2022)

## Built on by (most cited first, 30 of 98)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [LongNet: Scaling Transformers to 1,000,000,000 Tokens](https://mlsanity.com/paper/2307.02486/) (2023)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)
- [The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry](https://mlsanity.com/paper/2402.04347/) (2024)
- [Hierarchically Gated Recurrent Neural Network for Sequence Modeling](https://mlsanity.com/paper/2311.04823/) (2023)
- [In-Context Language Learning: Architectures and Algorithms](https://mlsanity.com/paper/2401.12973/) (2024)
- [Gated Slot Attention for Efficient Linear-Time Sequence Modeling](https://mlsanity.com/paper/2409.07146/) (2024)
- [Test-time regression: a unifying framework for designing sequence models with associative memory](https://mlsanity.com/paper/2501.12352/) (2025)
- [Lightning Attention-2: A Free Lunch for Handling Unlimited Sequence Lengths in Large Language Models](https://mlsanity.com/paper/2401.04658/) (2024)
- [Linearizing Large Language Models](https://mlsanity.com/paper/2405.06640/) (2024)
- [Bridging the Divide: Reconsidering Softmax and Linear Attention](https://mlsanity.com/paper/2412.06590/) (2024)
- [Hydra: Bidirectional State Space Models Through Generalized Matrix Mixers](https://mlsanity.com/paper/2407.09941/) (2024)
- [TransNormerLLM: A Faster and Better Large Language Model with Improved TransNormer](https://mlsanity.com/paper/2307.14995/) (2023)
- [Mixture of In-Context Prompters for Tabular PFNs](https://mlsanity.com/paper/2405.16156/) (2024)
- [On the Efficacy of Eviction Policy for Key-Value Constrained Generative Language Model Inference](https://mlsanity.com/paper/2402.06262/) (2024)
- [Various Lengths, Constant Speed: Efficient Language Modeling with Lightning Attention](https://mlsanity.com/paper/2405.17381/) (2024)
- [LoLCATs: On Low-Rank Linearizing of Large Language Models](https://mlsanity.com/paper/2410.10254/) (2024)
- [On Efficient Training of Large-Scale Deep Learning Models: A Literature Review](https://mlsanity.com/paper/2304.03589/) (2023)
- [Transformer-VQ: Linear-Time Transformers via Vector Quantization](https://mlsanity.com/paper/2309.16354/) (2023)
- [Efficient Attention via Control Variates](https://mlsanity.com/paper/2302.04542/) (2023)
- [MetaLA: Unified Optimal Linear Approximation to Softmax Attention Map](https://mlsanity.com/paper/2411.10741/) (2024)
- [Position: The Future of Bayesian Prediction Is Prior-Fitted](https://mlsanity.com/paper/2505.23947/) (2025)
- [Lattice: Learning to Efficiently Compress the Memory](https://mlsanity.com/paper/2504.05646/) (2025)
- [Fine-grained Audible Video Description](https://mlsanity.com/paper/2303.15616/) (2023)
- [Linearized Relative Positional Encoding](https://mlsanity.com/paper/2307.09270/) (2023)

## Abstract (arXiv)

Linear transformers aim to reduce the quadratic space-time complexity of vanilla transformers. However, they usually suffer from degraded performances on various tasks and corpus. In this paper, we examine existing kernel-based linear transformers and identify two key issues that lead to such performance gaps: 1) unbounded gradients in the attention computation adversely impact the convergence of linear transformer models; 2) attention dilution which trivially distributes attention scores over long sequences while neglecting neighbouring structures. To address these issues, we first identify that the scaling of attention matrices is the devil in unbounded gradients, which turns out unnecessary in linear attention as we show theoretically and empirically. To this end, we propose a new linear attention that replaces the scaling operation with a normalization to stabilize gradients. For the issue of attention dilution, we leverage a diagonal attention to confine attention to only neighbouring tokens in early layers. Benefiting from the stable gradients and improved attention, our new linear transformer model, transNormer, demonstrates superior performance on text classification and language modeling tasks, as well as on the challenging Long-Range Arena benchmark, surpassing vanilla transformer and existing linear variants by a clear margin while being significantly more space-time efficient. The code is available at https://github.com/OpenNLPLab/Transnormer .