Time series saliency maps: explaining models across multiple domains

2025-05-19

AI Summary

Traditional time-domain saliency maps struggle to capture semantically critical non-temporal features—such as spectral components—in time series. To address this, we propose Cross-Domain Integrated Gradients (CD-IG), the first extension of integrated gradients to the complex domain and general invertible differentiable transform domains (e.g., short-time Fourier transform), rigorously preserving path independence and attribution completeness. CD-IG establishes a unified cross-domain attribution framework enabling joint interpretation across time, frequency, and other complementary domains. Evaluated on heartbeat extraction, seizure detection, and zero-shot time-series forecasting, CD-IG consistently identifies semantically essential features overlooked by purely time-domain methods, substantially enhancing model interpretability. The method is publicly available with plug-and-play TensorFlow and PyTorch implementations.

Technology Category

• Computer Vision: Interpretability, Explainability, and Transparency
• Machine Learning: Time-Series/Data Streams
• Application Domains: Humanities & Computational Social Science

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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 on 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. Our approach reveals interpretable, problem-specific attributions that time-domain methods cannot capture, on three real-world tasks: wearable sensor heart rate extraction, electroencephalography-based seizure detection, and zero-shot time-series forecasting. 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 in time-series models that are impossible with traditional time-domain saliency.

Problem

• Explaining time-series models across multiple domains
• Extending saliency maps to frequency-based attributions
• Providing interpretable insights for real-world time-series tasks

Innovation

• Generalizes Integrated Gradients for cross-domain feature attribution
• Extends Integrated Gradients into the complex frequency domain
• Provides open-source library for plug-and-play cross-domain explainability