# Infomaxformer: Maximum Entropy Transformer for Long Time-Series Forecasting Problem

arXiv: https://arxiv.org/abs/2301.01772 · HTML: https://mlsanity.com/paper/2301.01772/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 66 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Builds on (most cited first, 30 of 43)

- [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)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (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)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [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)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [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)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [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)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)

## Built on by (most cited first, 5 of 5)

- [Deep Learning for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2503.10198/) (2025)
- [Not All Frequencies Are Created Equal:Towards a Dynamic Fusion of Frequencies in Time-Series Forecasting](https://mlsanity.com/paper/2407.12415/) (2024)
- [Understanding Token-level Topological Structures in Transformer-based Time Series Forecasting](https://mlsanity.com/paper/2404.10337/) (2024)
- [Beyond All-to-All: Causal-Aligned Transformer with Dynamic Structure Learning for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.16308/) (2025)
- [Fewer yet critical: Reducing Redundant Token Dependencies for Transformer-based Time Series Forecasting](https://mlsanity.com/paper/2503.06867/) (2025)

## Abstract (arXiv)

The Transformer architecture yields state-of-the-art results in many tasks such as natural language processing (NLP) and computer vision (CV), since the ability to efficiently capture the precise long-range dependency coupling between input sequences. With this advanced capability, however, the quadratic time complexity and high memory usage prevents the Transformer from dealing with long time-series forecasting problem (LTFP). To address these difficulties: (i) we revisit the learned attention patterns of the vanilla self-attention, redesigned the calculation method of self-attention based the Maximum Entropy Principle. (ii) we propose a new method to sparse the self-attention, which can prevent the loss of more important self-attention scores due to random sampling.(iii) We propose Keys/Values Distilling method motivated that a large amount of feature in the original self-attention map is redundant, which can further reduce the time and spatial complexity and make it possible to input longer time-series. Finally, we propose a method that combines the encoder-decoder architecture with seasonal-trend decomposition, i.e., using the encoder-decoder architecture to capture more specific seasonal parts. A large number of experiments on several large-scale datasets show that our Infomaxformer is obviously superior to the existing methods. We expect this to open up a new solution for Transformer to solve LTFP, and exploring the ability of the Transformer architecture to capture much longer temporal dependencies.