# Gated Delta Networks: Improving Mamba2 with Delta Rule

arXiv: https://arxiv.org/abs/2412.06464 · HTML: https://mlsanity.com/paper/2412.06464/

## Key facts

- Cited by 532 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 100 references that are in the map.
- First posted on arXiv 9 Dec 2024.

## Builds on (most cited first, 30 of 73)

- [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)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [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)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [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)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [The NarrativeQA Reading Comprehension Challenge](https://mlsanity.com/paper/1712.07040/) (2017)
- [SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization](https://mlsanity.com/paper/1911.12237/) (2019)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [A Dataset of Information-Seeking Questions and Answers Anchored in Research Papers](https://mlsanity.com/paper/2105.03011/) (2021)
- [Multi-News: a Large-Scale Multi-Document Summarization Dataset and Abstractive Hierarchical Model](https://mlsanity.com/paper/1906.01749/) (2019)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)

## Built on by (most cited first, 30 of 532)

- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [Kimi K3: Open Frontier Intelligence](https://mlsanity.com/paper/2607.24653/) (2026)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [Sparse VideoGen2: Accelerate Video Generation with Sparse Attention via Semantic-Aware Permutation](https://mlsanity.com/paper/2505.18875/) (2025)
- [One-Minute Video Generation with Test-Time Training](https://mlsanity.com/paper/2504.05298/) (2025)
- [Mamba-3: Improved Sequence Modeling using State Space Principles](https://mlsanity.com/paper/2603.15569/) (2026)
- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [DeltaProduct: Improving State-Tracking in Linear RNNs via Householder Products](https://mlsanity.com/paper/2502.10297/) (2025)
- [Test-time regression: a unifying framework for designing sequence models with associative memory](https://mlsanity.com/paper/2501.12352/) (2025)
- [Dynamic Chunking for End-to-End Hierarchical Sequence Modeling](https://mlsanity.com/paper/2507.07955/) (2025)
- [Nested Learning: The Illusion of Deep Learning Architectures](https://mlsanity.com/paper/2512.24695/) (2025)
- [SageAttention3: Microscaling FP4 Attention for Inference and An Exploration of 8-Bit Training](https://mlsanity.com/paper/2505.11594/) (2025)
- [ATLAS: Learning to Optimally Memorize the Context at Test Time](https://mlsanity.com/paper/2505.23735/) (2025)
- [Attention Residuals](https://mlsanity.com/paper/2603.15031/) (2026)
- [It's All Connected: A Journey Through Test-Time Memorization, Attentional Bias, Retention, and Online Optimization](https://mlsanity.com/paper/2504.13173/) (2025)
- [Long-Context State-Space Video World Models](https://mlsanity.com/paper/2505.20171/) (2025)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [End-to-End Test-Time Training for Long Context](https://mlsanity.com/paper/2512.23675/) (2025)
- [SLA: Beyond Sparsity in Diffusion Transformers via Fine-Tunable Sparse-Linear Attention](https://mlsanity.com/paper/2509.24006/) (2025)
- [SANA-WM: Efficient Minute-Scale World Modeling with Hybrid Linear Diffusion Transformer](https://mlsanity.com/paper/2605.15178/) (2026)
- [MoM: Linear Sequence Modeling with Mixture-of-Memories](https://mlsanity.com/paper/2502.13685/) (2025)
- [MesaNet: Sequence Modeling by Locally Optimal Test-Time Training](https://mlsanity.com/paper/2506.05233/) (2025)
- [MiniMax Sparse Attention](https://mlsanity.com/paper/2606.13392/) (2026)
- [Baichuan-M1: Pushing the Medical Capability of Large Language Models](https://mlsanity.com/paper/2502.12671/) (2025)
- [VideoSSM: Autoregressive Long Video Generation with Hybrid State-Space Memory](https://mlsanity.com/paper/2512.04519/) (2025)
- [Jet-Nemotron: Efficient Language Model with Post Neural Architecture Search](https://mlsanity.com/paper/2508.15884/) (2025)
- [Log-Linear Attention](https://mlsanity.com/paper/2506.04761/) (2025)

## Abstract (arXiv)

Linear Transformers have gained attention as efficient alternatives to standard Transformers, but their performance in retrieval and long-context tasks has been limited. To address these limitations, recent work has explored two distinct mechanisms: gating for adaptive memory control and the delta update rule for precise memory modifications. We observe that these mechanisms are complementary: gating enables rapid memory erasure while the delta rule facilitates targeted updates. Building on this insight, we introduce the gated delta rule and develop a parallel training algorithm optimized for modern hardware. Our proposed architecture, Gated DeltaNet, consistently surpasses existing models like Mamba2 and DeltaNet across multiple benchmarks, including language modeling, common-sense reasoning, in-context retrieval, length extrapolation, and long-context understanding. We further enhance performance by developing hybrid architectures that combine Gated DeltaNet layers with sliding window attention or Mamba2 layers, achieving both improved training efficiency and superior task performance.