# PENGUIN: Enhancing Transformer with Periodic-Nested Group Attention for Long-term Time Series Forecasting

arXiv: https://arxiv.org/abs/2508.13773 · HTML: https://mlsanity.com/paper/2508.13773/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 65 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 30 of 36)

- [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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting](https://mlsanity.com/paper/2310.09751/) (2023)
- [jina-embeddings-v3: Multilingual Embeddings With Task LoRA](https://mlsanity.com/paper/2409.10173/) (2024)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [AutoTimes: Autoregressive Time Series Forecasters via Large Language Models](https://mlsanity.com/paper/2402.02370/) (2024)
- [EEGFormer: Towards Transferable and Interpretable Large-Scale EEG Foundation Model](https://mlsanity.com/paper/2401.10278/) (2024)

## Built on by (most cited first, 3 of 3)

- [The Geometric Inductive Bias of Grokking: Bypassing Phase Transitions via Architectural Topology](https://mlsanity.com/paper/2603.05228/) (2026)
- [Fighter: Unveiling the Graph Convolutional Nature of Transformers in Time Series Modeling](https://mlsanity.com/paper/2510.17106/) (2025)
- [Beyond Static Positional Encoding: Bayesian Time-aware Attention for Non-Stationary Long-term Time Series Forecasting](https://mlsanity.com/paper/2610.19603/) (2026)

## Abstract (arXiv)

Despite advances in the Transformer architecture, their effectiveness for long-term time series forecasting (LTSF) remains controversial. In this paper, we investigate the potential of integrating explicit periodicity modeling into the self-attention mechanism to enhance the performance of Transformer-based architectures for LTSF. Specifically, we propose PENGUIN, a simple yet effective periodic-nested group attention mechanism. Our approach introduces a periodic-aware relative attention bias to directly capture periodic structures and a grouped multi-query attention mechanism to handle multiple coexisting periodicities (e.g., daily and weekly cycles) within time series data. Extensive experiments across diverse benchmarks demonstrate that PENGUIN consistently outperforms both MLP-based and Transformer-based models. Code is available at https://github.com/ysygMhdxw/AISTATS2026_PENGUIN.