# Hierarchically Gated Recurrent Neural Network for Sequence Modeling

arXiv: https://arxiv.org/abs/2311.04823 · HTML: https://mlsanity.com/paper/2311.04823/

## Key facts

- Cited by 102 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 81 references that are in the map.
- First posted on arXiv 8 Nov 2023.

## Builds on (most cited first, 30 of 67)

- [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)
- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [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)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [AST: Audio Spectrogram Transformer](https://mlsanity.com/paper/2104.01778/) (2021)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [VATT: Transformers for Multimodal Self-Supervised Learning from Raw Video, Audio and Text](https://mlsanity.com/paper/2104.11178/) (2021)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)

## Built on by (most cited first, 30 of 102)

- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [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)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Data Engineering for Scaling Language Models to 128K Context](https://mlsanity.com/paper/2402.10171/) (2024)
- [Lessons from the Trenches on Reproducible Evaluation of Language Models](https://mlsanity.com/paper/2405.14782/) (2024)
- [Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling](https://mlsanity.com/paper/2406.07522/) (2024)
- [Eagle and Finch: RWKV with Matrix-Valued States and Dynamic Recurrence](https://mlsanity.com/paper/2404.05892/) (2024)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)
- [Vision-RWKV: Efficient and Scalable Visual Perception with RWKV-Like Architectures](https://mlsanity.com/paper/2403.02308/) (2024)
- [Gated Slot Attention for Efficient Linear-Time Sequence Modeling](https://mlsanity.com/paper/2409.07146/) (2024)
- [Diffusion Models Without Attention](https://mlsanity.com/paper/2311.18257/) (2023)
- [Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges](https://mlsanity.com/paper/2404.16112/) (2024)
- [Longhorn: State Space Models are Amortized Online Learners](https://mlsanity.com/paper/2407.14207/) (2024)
- [Lightning Attention-2: A Free Lunch for Handling Unlimited Sequence Lengths in Large Language Models](https://mlsanity.com/paper/2401.04658/) (2024)
- [DiG: Scalable and Efficient Diffusion Models with Gated Linear Attention](https://mlsanity.com/paper/2405.18428/) (2024)
- [Forgetting Transformer: Softmax Attention with a Forget Gate](https://mlsanity.com/paper/2503.02130/) (2025)
- [Base of RoPE Bounds Context Length](https://mlsanity.com/paper/2405.14591/) (2024)
- [DeciMamba: Exploring the Length Extrapolation Potential of Mamba](https://mlsanity.com/paper/2406.14528/) (2024)
- [MoM: Linear Sequence Modeling with Mixture-of-Memories](https://mlsanity.com/paper/2502.13685/) (2025)
- [The Expressive Capacity of State Space Models: A Formal Language Perspective](https://mlsanity.com/paper/2405.17394/) (2024)
- [Diffusion-RWKV: Scaling RWKV-Like Architectures for Diffusion Models](https://mlsanity.com/paper/2404.04478/) (2024)
- [Jet-Nemotron: Efficient Language Model with Post Neural Architecture Search](https://mlsanity.com/paper/2508.15884/) (2025)
- [MambaMixer: Efficient Selective State Space Models with Dual Token and Channel Selection](https://mlsanity.com/paper/2403.19888/) (2024)
- [LION: Linear Group RNN for 3D Object Detection in Point Clouds](https://mlsanity.com/paper/2407.18232/) (2024)
- [Physics of Language Models: Part 4.1, Architecture Design and the Magic of Canon Layers](https://mlsanity.com/paper/2512.17351/) (2025)
- [MambaLRP: Explaining Selective State Space Sequence Models](https://mlsanity.com/paper/2406.07592/) (2024)
- [Various Lengths, Constant Speed: Efficient Language Modeling with Lightning Attention](https://mlsanity.com/paper/2405.17381/) (2024)
- [Scalable MatMul-free Language Modeling](https://mlsanity.com/paper/2406.02528/) (2024)

## Abstract (arXiv)

Transformers have surpassed RNNs in popularity due to their superior abilities in parallel training and long-term dependency modeling. Recently, there has been a renewed interest in using linear RNNs for efficient sequence modeling. These linear RNNs often employ gating mechanisms in the output of the linear recurrence layer while ignoring the significance of using forget gates within the recurrence. In this paper, we propose a gated linear RNN model dubbed Hierarchically Gated Recurrent Neural Network (HGRN), which includes forget gates that are lower bounded by a learnable value. The lower bound increases monotonically when moving up layers. This allows the upper layers to model long-term dependencies and the lower layers to model more local, short-term dependencies. Experiments on language modeling, image classification, and long-range arena benchmarks showcase the efficiency and effectiveness of our proposed model. The source code is available at https://github.com/OpenNLPLab/HGRN.