Time series saliency maps: Explaining models across multiple domains

Traditional saliency map methods, popularized in computer vision, highlight individual input points that contribute most to a model's output. However, in the context of time series, they offer limited insights because semantically meaningful features are often found in other domains. Thus, we introduce in this paper Cross-domain Integrated Gradients, a generalization of Integrated Gradients that enables feature attributions in any domain formulated as an invertible, differentiable transformation of the time domain. Our derivation extends Integrated Gradients into complex-valued domains, enabling frequency-based attributions, while preserving path independence and completeness. We validate our method via controlled mechanistic experiments, quantitative faithfulness and perturbation-stability tests, and real-world case studies. Across wearable heart-rate extraction, EEG-based seizure detection, and zero-shot forecasting, our proposed Cross-domain Integrated Gradients approach identifies whether predictions rely on heart-rate frequencies or interference, epileptic sources or artifacts, and trend or seasonal components, revealing model behaviour that time-domain saliency does not capture. We release an open-source library with TensorFlow, native PyTorch, and Captum support for plug-and-play cross-domain explainability of time-series models.

Machine learning models are increasingly used to analyze time-series data, measurement collected over time, such as heart signals from wearables, brain activity recordings, and data used to forecast future trends. However, it is often difficult to understand what information these models use to make a prediction. Standard explanation methods usually highlight individual time points, but in time-series data the meaningful information may instead appear as frequencies, hidden signal sources, trends, or seasonal patterns. We introduce Cross-domain Integrated Gradients, a method that explains time-series models in a user-chosen signal domain rather than only in time. This allows practitioners to ask more meaningful questions: whether a heart-rate model relies on true heart rhythms or motion noise, whether a seizure detector uses epileptic brain activity or artefacts, and whether a forecasting model captures trend or seasonality. Our experiments show that these domain-specific explanations can reveal model behavior that standard time-based explanations miss. We also provide an open-source library with TensorFlow, PyTorch, and Captum support for broader use.