# Explaining Time Series Forecasting with Horizon-Resolved Attribution

arXiv: https://arxiv.org/abs/2609.12639 · HTML: https://mlsanity.com/paper/2609.12639/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 58 of its 65 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Builds on (most cited first, 30 of 58)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [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)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [ERASER: A Benchmark to Evaluate Rationalized NLP Models](https://mlsanity.com/paper/1911.03429/) (2019)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [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)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)

## Abstract (arXiv)

Recent advances in explaining time series (TS) models have produced methods that identify which past values a prediction depends on. However, most existing methods return a single importance vector, assuming that every predicted step depends on the same past values. In this paper, we show that this assumption does not hold, as different forecast steps depend on different past values. Motivated by this observation, we propose Horizon-Resolved eXplanation (HRX), which adds a horizon axis to the explanation, so that every forecast step receives its own importance map. HRX is a simple yet effective plug-in framework with three components: 1) an estimator that reads these maps out of any differentiable forecaster without modifying the TS backbone, 2) an evaluation protocol that validates the horizon axis by measuring how much a single forecast step changes when the inputs an importance map ranks highest are removed, and 3) a rank criterion that predicts in advance whether the axis is worth resolving on a given TS. We further show that this step-wise dependence is low-dimensional, as the explanations of all steps are built from a few shared maps whose number does not grow with the forecast length. Extensive experiments across various backbones and datasets show that the improvement comes from the horizon axis and holds for estimators of previous explanation methods. Code is available at https://github.com/seunghan96/HRX.