# Time series saliency maps: explaining models across multiple domains

arXiv: https://arxiv.org/abs/2505.13100 · HTML: https://mlsanity.com/paper/2505.13100/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 45 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 22 of 22)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Visualizing and Understanding Neural Models in NLP](https://mlsanity.com/paper/1506.01066/) (2015)
- [Benchmarking Deep Learning Interpretability in Time Series Predictions](https://mlsanity.com/paper/2010.13924/) (2020)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [AudioMNIST: Exploring Explainable Artificial Intelligence for Audio Analysis on a Simple Benchmark](https://mlsanity.com/paper/1807.03418/) (2018)
- [Encoding Time-Series Explanations through Self-Supervised Model Behavior Consistency](https://mlsanity.com/paper/2306.02109/) (2023)
- [TimeX++: Learning Time-Series Explanations with Information Bottleneck](https://mlsanity.com/paper/2405.09308/) (2024)
- [Explainable AI for Time Series via Virtual Inspection Layers](https://mlsanity.com/paper/2303.06365/) (2023)
- [IDGI: A Framework to Eliminate Explanation Noise from Integrated Gradients](https://mlsanity.com/paper/2303.14242/) (2023)
- [Sanity Simulations for Saliency Methods](https://mlsanity.com/paper/2105.06506/) (2021)
- [Deletion and Insertion Tests in Regression Models](https://mlsanity.com/paper/2205.12423/) (2022)
- [New Definitions and Evaluations for Saliency Methods: Staying Intrinsic, Complete and Sound](https://mlsanity.com/paper/2211.02912/) (2022)
- [KID-PPG: Knowledge Informed Deep Learning for Extracting Heart Rate from a Smartwatch](https://mlsanity.com/paper/2405.09559/) (2024)
- [Time is Not Enough: Time-Frequency based Explanation for Time-Series Black-Box Models](https://mlsanity.com/paper/2408.03636/) (2024)
- [FLEXtime: Filterbank learning to explain time series](https://mlsanity.com/paper/2411.05841/) (2024)
- [The Blame Problem in Evaluating Local Explanations, and How to Tackle it](https://mlsanity.com/paper/2310.03466/) (2023)
- [FreqRISE: Explaining time series using frequency masking](https://mlsanity.com/paper/2406.13584/) (2024)
- [DC is all you need: describing ReLU from a signal processing standpoint](https://mlsanity.com/paper/2407.16556/) (2024)

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

- [Dissecting Chronos: Sparse Autoencoders Reveal Causal Feature Hierarchies in Time Series Foundation Models](https://mlsanity.com/paper/2603.10071/) (2026)
- [Attribution and Uncertainty Behavior of Learned Residual Gyro Correction for Gyro-Stellar Estimation](https://mlsanity.com/paper/2607.24608/) (2026)

## Abstract (arXiv)

Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time series, they offer limited insights, as semantically meaningful features are often found in other domains. We introduce Cross-domain Integrated Gradients, a generalization of Integrated Gradients. Our method enables feature attributions in any domain that can be formulated as an invertible, differentiable transformation of the time domain. Crucially, our derivation extends the original Integrated Gradients into the complex domain, enabling frequency-based attributions. We provide the necessary theoretical guarantees, namely, path independence and completeness. We validate our method via controlled experiments with mechanistic analysis, quantitative faithfulness tests, and real-world case studies. Our approach reveals interpretable, problem-specific attributions that time-domain methods cannot capture in three real-world tasks across a variety of model architectures, machine-learning tasks, and cross-domain transforms: frequency-based attribution for a regression task in wearable heart rate extraction, independent component analysis in a classification task for electroencephalography-based seizure detection, and seasonal-trend decomposition for a forecasting problem with a zero-shot time-series foundation model. We release an open-source TensorFlow/PyTorch library to enable plug-and-play cross-domain explainability for time-series models. These results demonstrate the ability of Cross-Domain Integrated Gradients to provide semantically meaningful insights into time-series models that are impossible to achieve with traditional saliency in the time domain.