# Efficient Linear Attention for Multivariate Time Series Modeling via Entropy Equality

arXiv: https://arxiv.org/abs/2511.03190 · HTML: https://mlsanity.com/paper/2511.03190/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2206.09112/) (2022)
- [Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.09113/) (2022)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [Spatial-Temporal-Decoupled Masked Pre-training for Spatiotemporal Forecasting](https://mlsanity.com/paper/2312.00516/) (2023)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [Spatiotemporal-aware Trend-Seasonality Decomposition Network for Traffic Flow Forecasting](https://mlsanity.com/paper/2502.12213/) (2025)
- [Heterogeneity-Informed Meta-Parameter Learning for Spatiotemporal Time Series Forecasting](https://mlsanity.com/paper/2405.10800/) (2024)
- [Dynamic Frequency Domain Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/2312.11933/) (2023)

## Abstract (arXiv)

Attention mechanisms have been extensively employed in various applications, including time series modeling, owing to their capacity to capture intricate dependencies; however, their utility is often constrained by quadratic computational complexity, which impedes scalability for long sequences. In this work, we propose a novel linear attention mechanism designed to overcome these limitations. Our approach is grounded in a theoretical demonstration that entropy, as a strictly concave function on the probability simplex, implies that distributions with aligned probability rankings and similar entropy values exhibit structural resemblance. Building on this insight, we develop an efficient approximation algorithm that computes the entropy of dot-product-derived distributions with only linear complexity, enabling the implementation of a linear attention mechanism based on entropy equality. Through rigorous analysis, we reveal that the effectiveness of attention in spatio-temporal time series modeling may not primarily stem from the non-linearity of softmax but rather from the attainment of a moderate and well-balanced weight distribution. Extensive experiments on four spatio-temporal datasets validate our method, demonstrating competitive or superior forecasting performance while achieving substantial reductions in both memory usage and computational time.