# CyFA: Linear Sequence Modeling with Relative-Time-Partitioned Memory

arXiv: https://arxiv.org/abs/2609.36259 · HTML: https://mlsanity.com/paper/2609.36259/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 62 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [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)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [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)
- [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)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (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)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [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)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (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)
- [RWKV-7 "Goose" with Expressive Dynamic State Evolution](https://mlsanity.com/paper/2503.14456/) (2025)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)
- [Language Models Enable Simple Systems for Generating Structured Views of Heterogeneous Data Lakes](https://mlsanity.com/paper/2304.09433/) (2023)
- [The Devil in Linear Transformer](https://mlsanity.com/paper/2210.10340/) (2022)

## Abstract (arXiv)

Linear RNNs offer linear-time sequence processing and constant-memory decoding, but their fixed-size recurrent states must accommodate all past key--value associations. Existing forgetting mechanisms and Delta Rule updates reduce interference by selectively clearing or correcting the state, yet earlier associations can still become difficult to retrieve. We introduce CyFA (Cyclic Flow Attention), a Linear RNN with relative-time-partitioned memory. At each step, a learned clock controls the cyclic transport applied jointly to the key and value states before the current key--value pair enters the age-zero slot, thereby organizing stored associations across relative-time slots. We further derive an exact change to absolute-clock coordinates that expresses CyFA as two scalar-decay linear attention recurrences and enables efficient chunk-wise training. Across 400M--1.4B pretraining experiments with matched recurrent-state sizes, CyFA improves recall-intensive performance while maintaining competitive language modeling and high computational efficiency. At 400M, CyFA outperforms KDA on FDA (42.60 vs. 26.07) while requiring only 46.7% and 48.3% of KDA's forward and backward core-operator execution times, respectively. Our code is publicly available at hrefhttps://github.com/Chyxx/CyclicFlowAttentionthis https URL.