# Going Beyond Linear Transformers with Recurrent Fast Weight Programmers

arXiv: https://arxiv.org/abs/2106.06295 · HTML: https://mlsanity.com/paper/2106.06295/

## Key facts

- Cited by 89 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 84 references that are in the map.
- First posted on arXiv 11 Jun 2021.

## Builds on (most cited first, 30 of 57)

- [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)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [Agent57: Outperforming the Atari Human Benchmark](https://mlsanity.com/paper/2003.13350/) (2020)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [Stabilizing Transformers for Reinforcement Learning](https://mlsanity.com/paper/1910.06764/) (2019)

## Built on by (most cited first, 30 of 89)

- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (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)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [TransDreamer: Reinforcement Learning with Transformer World Models](https://mlsanity.com/paper/2202.09481/) (2022)
- [The Mamba in the Llama: Distilling and Accelerating Hybrid Models](https://mlsanity.com/paper/2408.15237/) (2024)
- [The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry](https://mlsanity.com/paper/2402.04347/) (2024)
- [The Devil is in the Detail: Simple Tricks Improve Systematic Generalization of Transformers](https://mlsanity.com/paper/2108.12284/) (2021)
- [Block-Recurrent Transformers](https://mlsanity.com/paper/2203.07852/) (2022)
- [General-Purpose In-Context Learning by Meta-Learning Transformers](https://mlsanity.com/paper/2212.04458/) (2022)
- [Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues](https://mlsanity.com/paper/2411.12537/) (2024)
- [One-Minute Video Generation with Test-Time Training](https://mlsanity.com/paper/2504.05298/) (2025)
- [Gated Slot Attention for Efficient Linear-Time Sequence Modeling](https://mlsanity.com/paper/2409.07146/) (2024)
- [Nested Learning: The Illusion of Deep Learning Architectures](https://mlsanity.com/paper/2512.24695/) (2025)
- [ATLAS: Learning to Optimally Memorize the Context at Test Time](https://mlsanity.com/paper/2505.23735/) (2025)
- [It's All Connected: A Journey Through Test-Time Memorization, Attentional Bias, Retention, and Online Optimization](https://mlsanity.com/paper/2504.13173/) (2025)
- [The Neural Data Router: Adaptive Control Flow in Transformers Improves Systematic Generalization](https://mlsanity.com/paper/2110.07732/) (2021)
- [End-to-End Test-Time Training for Long Context](https://mlsanity.com/paper/2512.23675/) (2025)
- [A Survey on Transformers in Reinforcement Learning](https://mlsanity.com/paper/2301.03044/) (2023)
- [Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiation](https://mlsanity.com/paper/2207.00787/) (2022)
- [A Modern Self-Referential Weight Matrix That Learns to Modify Itself](https://mlsanity.com/paper/2202.05780/) (2022)
- [On Transforming Reinforcement Learning by Transformer: The Development Trajectory](https://mlsanity.com/paper/2212.14164/) (2022)
- [Gated DeltaNet-2: Decoupling Erase and Write in Linear Attention](https://mlsanity.com/paper/2605.22791/) (2026)
- [Efficient Attention via Control Variates](https://mlsanity.com/paper/2302.04542/) (2023)
- [Meta-Learning Fast Weight Language Models](https://mlsanity.com/paper/2212.02475/) (2022)
- [Practical Computational Power of Linear Transformers and Their Recurrent and Self-Referential Extensions](https://mlsanity.com/paper/2310.16076/) (2023)
- [SARA-RT: Scaling up Robotics Transformers with Self-Adaptive Robust Attention](https://mlsanity.com/paper/2312.01990/) (2023)
- [Exploring the Promise and Limits of Real-Time Recurrent Learning](https://mlsanity.com/paper/2305.19044/) (2023)

## Abstract (arXiv)

Transformers with linearised attention (''linear Transformers'') have demonstrated the practical scalability and effectiveness of outer product-based Fast Weight Programmers (FWPs) from the '90s. However, the original FWP formulation is more general than the one of linear Transformers: a slow neural network (NN) continually reprograms the weights of a fast NN with arbitrary architecture. In existing linear Transformers, both NNs are feedforward and consist of a single layer. Here we explore new variations by adding recurrence to the slow and fast nets. We evaluate our novel recurrent FWPs (RFWPs) on two synthetic algorithmic tasks (code execution and sequential ListOps), Wikitext-103 language models, and on the Atari 2600 2D game environment. Our models exhibit properties of Transformers and RNNs. In the reinforcement learning setting, we report large improvements over LSTM in several Atari games. Our code is public.