# PETformer: Long-term Time Series Forecasting via Placeholder-enhanced Transformer

arXiv: https://arxiv.org/abs/2308.04791 · HTML: https://mlsanity.com/paper/2308.04791/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 54 references that are in the map.
- First posted on arXiv 9 Aug 2023.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)

## Built on by (most cited first, 22 of 22)

- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [AVA-VLA: Improving Vision-Language-Action models with Active Visual Attention](https://mlsanity.com/paper/2511.18960/) (2025)
- [PatchMixer: A Patch-Mixing Architecture for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2310.00655/) (2023)
- [Parametric Augmentation for Time Series Contrastive Learning](https://mlsanity.com/paper/2402.10434/) (2024)
- [MCformer: Multivariate Time Series Forecasting with Mixed-Channels Transformer](https://mlsanity.com/paper/2403.09223/) (2024)
- [Deep Learning for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2503.10198/) (2025)
- [Sparse-VQ Transformer: An FFN-Free Framework with Vector Quantization for Enhanced Time Series Forecasting](https://mlsanity.com/paper/2402.05830/) (2024)
- [Towards Lightweight Time Series Forecasting: a Patch-wise Transformer with Weak Data Enriching](https://mlsanity.com/paper/2501.10448/) (2025)
- [TFKAN: Time-Frequency KAN for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2506.12696/) (2025)
- [Enhancing Multivariate Time Series Forecasting with Mutual Information-driven Cross-Variable and Temporal Modeling](https://mlsanity.com/paper/2403.00869/) (2024)
- [Partial-Multivariate Model for Forecasting](https://mlsanity.com/paper/2408.09703/) (2024)
- [MFRS: A Multi-Frequency Reference Series Approach to Scalable and Accurate Time-Series Forecasting](https://mlsanity.com/paper/2503.08328/) (2025)
- [IndexNet: Timestamp and Variable-Aware Modeling for Time Series Forecasting](https://mlsanity.com/paper/2509.23813/) (2025)
- [Hydra: Dual Exponentiated Memory for Multivariate Time Series Analysis](https://mlsanity.com/paper/2511.00989/) (2025)
- [CEDAR: Controlled and Event-Driven Demand Forecasting via Residual Decomposition](https://mlsanity.com/paper/2608.25871/) (2026)
- [Crime Forecasting: A Spatio-temporal Analysis with Deep Learning Models](https://mlsanity.com/paper/2502.07465/) (2025)
- [InvDec: Inverted Decoder for Multivariate Time Series Forecasting with Separated Temporal and Variate Modeling](https://mlsanity.com/paper/2510.20302/) (2025)
- [AltTS: A Dual-Path Framework with Alternating Optimization for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.11533/) (2026)

## Abstract (arXiv)

Recently, the superiority of Transformer for long-term time series forecasting (LTSF) tasks has been challenged, particularly since recent work has shown that simple models can outperform numerous Transformer-based approaches. This suggests that a notable gap remains in fully leveraging the potential of Transformer in LTSF tasks. Consequently, this study investigates key issues when applying Transformer to LTSF, encompassing aspects of temporal continuity, information density, and multi-channel relationships. We introduce the Placeholder-enhanced Technique (PET) to enhance the computational efficiency and predictive accuracy of Transformer in LTSF tasks. Furthermore, we delve into the impact of larger patch strategies and channel interaction strategies on Transformer's performance, specifically Long Sub-sequence Division (LSD) and Multi-channel Separation and Interaction (MSI). These strategies collectively constitute a novel model termed PETformer. Extensive experiments have demonstrated that PETformer achieves state-of-the-art performance on eight commonly used public datasets for LTSF, surpassing all existing models. The insights and enhancement methodologies presented in this paper serve as valuable reference points and sources of inspiration for future research endeavors.