# Time-Series Forecasting via Topological Information Supervised Framework with Efficient Topological Feature Learning

arXiv: https://arxiv.org/abs/2503.23757 · HTML: https://mlsanity.com/paper/2503.23757/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 84 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [State-of-the-Art in the Architecture, Methods and Applications of StyleGAN](https://mlsanity.com/paper/2202.14020/) (2022)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [The persistence landscape and some of its properties](https://mlsanity.com/paper/1810.04963/) (2018)
- [Cliques and Cavities in the Human Connectome](https://mlsanity.com/paper/1608.03520/) (2016)
- [A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification](https://mlsanity.com/paper/1908.06856/) (2019)
- [TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images](https://mlsanity.com/paper/2101.08398/) (2021)
- [Persistence Codebooks for Topological Data Analysis](https://mlsanity.com/paper/1802.04852/) (2018)
- [Persistent Homology Meets Object Unity: Object Recognition in Clutter](https://mlsanity.com/paper/2305.03815/) (2023)
- [Unsupervised Space-Time Clustering using Persistent Homology](https://mlsanity.com/paper/1910.11525/) (2019)

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

- [Persistent Homology of Time Series through Complex Networks](https://mlsanity.com/paper/2605.01624/) (2026)
- [TopoPrimer: The Missing Topological Context in Forecasting Models](https://mlsanity.com/paper/2605.15035/) (2026)
- [TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting](https://mlsanity.com/paper/2606.25439/) (2026)

## Abstract (arXiv)

Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial modeling. Despite its success, the integration of TDA with time-series prediction remains underexplored due to three primary challenges: the limited utilization of temporal dependencies within topological features, computational bottlenecks associated with persistent homology, and the deterministic nature of TDA pipelines restricting generalized feature learning. This study addresses these challenges by proposing the Topological Information Supervised (TIS) Prediction framework, which leverages neural networks and Conditional Generative Adversarial Networks (CGANs) to generate synthetic topological features, preserving their distribution while significantly reducing computational time. We propose a novel training strategy that integrates topological consistency loss to improve the predictive accuracy of deep learning models. Specifically, we introduce two state-of-the-art models, TIS-BiGRU and TIS-Informer, designed to capture short-term and long-term temporal dependencies, respectively. Comparative experimental results demonstrate the superior performance of TIS models over conventional predictors, validating the effectiveness of integrating topological information. This work not only advances TDA-based time-series prediction but also opens new avenues for utilizing topological features in deep learning architectures.