# TopoCL: Topological Contrastive Learning for Time Series

arXiv: https://arxiv.org/abs/2502.02924 · HTML: https://mlsanity.com/paper/2502.02924/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 68 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 30 of 36)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Time-Series Representation Learning via Temporal and Contextual Contrasting](https://mlsanity.com/paper/2106.14112/) (2021)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency](https://mlsanity.com/paper/2206.08496/) (2022)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding](https://mlsanity.com/paper/2106.00750/) (2021)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [SimMTM: A Simple Pre-Training Framework for Masked Time-Series Modeling](https://mlsanity.com/paper/2302.00861/) (2023)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Mixing Up Contrastive Learning: Self-Supervised Representation Learning for Time Series](https://mlsanity.com/paper/2203.09270/) (2022)
- [Time Series Contrastive Learning with Information-Aware Augmentations](https://mlsanity.com/paper/2303.11911/) (2023)
- [TimesURL: Self-supervised Contrastive Learning for Universal Time Series Representation Learning](https://mlsanity.com/paper/2312.15709/) (2023)

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

- [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)
- [Structured Latent Space Modeling over Multi-Scale Temporal Patches for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2607.19404/) (2026)
- [Synergistic Fusion of Topological Structure and Temporal Semantics of Mobility for Urban Region Embedding](https://mlsanity.com/paper/2609.08268/) (2026)
- [HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2609.08286/) (2026)

## Abstract (arXiv)

Universal time series representation learning is challenging but valuable in real-world applications such as classification, anomaly detection, and forecasting. Recently, contrastive learning (CL) has been actively explored to tackle time series representation. However, a key challenge is that the data augmentation process in CL can distort seasonal patterns or temporal dependencies, inevitably leading to a loss of semantic information. To address this challenge, we propose Topological Contrastive Learning for time series (TopoCL). TopoCL mitigates such information loss by incorporating persistent homology, which captures the topological characteristics of data that remain invariant under transformations. In this paper, we treat the temporal and topological properties of time series data as distinct modalities. Specifically, we compute persistent homology to construct topological features of time series data, representing them in persistence diagrams. We then design a neural network to encode these persistent diagrams. Our approach jointly optimizes CL within the time modality and time-topology correspondence, promoting a comprehensive understanding of both temporal semantics and topological properties of time series. We conduct extensive experiments on four downstream tasks-classification, anomaly detection, forecasting, and transfer learning. The results demonstrate that TopoCL achieves state-of-the-art performance.