# Topological Attention for Time Series Forecasting

arXiv: https://arxiv.org/abs/2107.09031 · HTML: https://mlsanity.com/paper/2107.09031/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Connectivity-Optimized Representation Learning via Persistent Homology](https://mlsanity.com/paper/1906.09003/) (2019)
- [PI-Net: A Deep Learning Approach to Extract Topological Persistence Images](https://mlsanity.com/paper/1906.01769/) (2019)
- [Chatter Classification in Turning Using Machine Learning and Topological Data Analysis](https://mlsanity.com/paper/1804.02261/) (2018)
- [Cyclicality, Periodicity and the Topology of Time Series](https://mlsanity.com/paper/1905.12118/) (2019)

## Built on by (most cited first, 14 of 14)

- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Neural Approximation of Graph Topological Features](https://mlsanity.com/paper/2201.12032/) (2022)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [Temporal Saliency Detection Towards Explainable Transformer-based Timeseries Forecasting](https://mlsanity.com/paper/2212.07771/) (2022)
- [Latent Trajectory Dynamics in Large Language Models: A Manifold Evolution Framework with Empirical Validation](https://mlsanity.com/paper/2505.20340/) (2025)
- [An Adaptive GViT for Gas Mixture Identification and Concentration Estimation](https://mlsanity.com/paper/2303.05685/) (2023)
- [Late Meta-learning Fusion Using Representation Learning for Time Series Forecasting](https://mlsanity.com/paper/2303.11000/) (2023)
- [Topology-enhanced machine learning for speech signal processing](https://mlsanity.com/paper/2311.15210/) (2023)
- [Topological Persistence Guided Knowledge Distillation for Wearable Sensor Data](https://mlsanity.com/paper/2407.05315/) (2024)
- [Robust Short-Term OEE Forecasting in Industry 4.0 via Topological Data Analysis](https://mlsanity.com/paper/2507.02890/) (2025)
- [Global and Local Topology-Aware Attention with Persistent Homology and Euler Biases for Time-Series Forecasting](https://mlsanity.com/paper/2605.03163/) (2026)
- [TopoPrimer: The Missing Topological Context in Forecasting Models](https://mlsanity.com/paper/2605.15035/) (2026)
- [Velocity-coupled Representation Refinement for Satellite Orbit Prediction](https://mlsanity.com/paper/2608.23728/) (2026)

## Abstract (arXiv)

The problem of (point) forecasting  textitunivariate  time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time series observations. As an extension, we study whether textitlocal topological properties, as captured via persistent homology, can serve as a reliable signal that provides complementary information for learning to forecast. To this end, we propose textittopological attention, which allows attending to local topological features within a time horizon of historical data. Our approach easily integrates into existing end-to-end trainable forecasting models, such as textttN-BEATS, and in combination with the latter exhibits state-of-the-art performance on the large-scale M4 benchmark dataset of 100,000 diverse time series from different domains. Ablation experiments, as well as a comparison to a broad range of forecasting methods in a setting where only a single time series is available for training, corroborate the beneficial nature of including local topological information through an attention mechanism.