# ProtoTS: Learning Hierarchical Prototypes for Explainable Time Series Forecasting

arXiv: https://arxiv.org/abs/2509.23159 · HTML: https://mlsanity.com/paper/2509.23159/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 65 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [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)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [TransTab: Learning Transferable Tabular Transformers Across Tables](https://mlsanity.com/paper/2205.09328/) (2022)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [Infinite Mixture Prototypes for Few-Shot Learning](https://mlsanity.com/paper/1902.04552/) (2019)
- [Explaining Time Series Predictions with Dynamic Masks](https://mlsanity.com/paper/2106.05303/) (2021)
- [Interpretable and Steerable Sequence Learning via Prototypes](https://mlsanity.com/paper/1907.09728/) (2019)
- [Explainable Artificial Intelligence (XAI) on TimeSeries Data: A Survey](https://mlsanity.com/paper/2104.00950/) (2021)

## Built on by (most cited first, 2 of 2)

- [This Looks Distinctly Like That: Grounding Interpretable Recognition in Stiefel Geometry against Neural Collapse](https://mlsanity.com/paper/2603.08374/) (2026)
- [ConceptTS: LLM-Guided Concept Bottlenecks for Interpretable Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2608.21277/) (2026)

## Abstract (arXiv)

While deep learning has achieved impressive performance in time series forecasting, it becomes increasingly crucial to understand its decision-making process for building trust in high-stakes scenarios. Existing interpretable models often provide only local and partial explanations, lacking the capability to reveal how heterogeneous and interacting input variables jointly shape the overall temporal patterns in the forecast curve. We propose ProtoTS, a novel interpretable forecasting framework that achieves both high accuracy and transparent decision-making through modeling prototypical temporal patterns. ProtoTS computes instance-prototype similarity based on a denoised representation that preserves abundant heterogeneous information. The prototypes are organized hierarchically to capture global temporal patterns with coarse prototypes while capturing finer-grained local variations with detailed prototypes, enabling expert steering and multi-level interpretability. Experiments on multiple realistic benchmarks, including a newly released LOF dataset, show that ProtoTS not only exceeds existing methods in forecast accuracy but also delivers expert-steerable interpretations for better model understanding and decision support.