When, How Long and How Much? Interpretable Neural Networks for Time Series Regression by Learning to Mask and Aggregate

TL;DR

This work tackles the interpretability gap in time series extrinsic regression by introducing MAGNETS, a mask-and-aggregate neural architecture that discovers concepts without supervision. MAGNETS identifies input-dependent temporal regions via masks, aggregates them into a compact set of interpretable concepts, and combines them linearly to predict the target, enabling faithful, transparent reasoning. Across synthetic and real-world datasets, MAGNETS matches or exceeds interpretable baselines and remains competitive with black-box models, while delivering explanations that faithfully reflect temporal localization and multivariate interactions. This approach advances trustworthy TSER by providing both accurate predictions and easily inspectable, concept-based reasoning paths.

Abstract

Time series extrinsic regression (TSER) refers to the task of predicting a continuous target variable from an input time series. It appears in many domains, including healthcare, finance, environmental monitoring, and engineering. In these settings, accurate predictions and trustworthy reasoning are both essential. Although state-of-the-art TSER models achieve strong predictive performance, they typically operate as black boxes, making it difficult to understand which temporal patterns drive their decisions. Post-hoc interpretability techniques, such as feature attribution, aim to to explain how the model arrives at its predictions, but often produce coarse, noisy, or unstable explanations. Recently, inherently interpretable approaches based on concepts, additive decompositions, or symbolic regression, have emerged as promising alternatives. However, these approaches remain limited: they require explicit supervision on the concepts themselves, often cannot capture interactions between time-series features, lack expressiveness for complex temporal patterns, and struggle to scale to high-dimensional multivariate data. To address these limitations, we propose MAGNETS (Mask-and-AGgregate NEtwork for Time Series), an inherently interpretable neural architecture for TSER. MAGNETS learns a compact set of human-understandable concepts without requiring any annotations. Each concept corresponds to a learned, mask-based aggregation over selected input features, explicitly revealing both which features drive predictions and when they matter in the sequence. Predictions are formed as combinations of these learned concepts through a transparent, additive structure, enabling clear insight into the model's decision process.

Figures (5)

• Figure 1: Overview of the proposed MAGNETS architecture for interpretable TSER. (A) Given an input multivariate time series, the mask generation network produces a set of logits (Eq. \ref{['eq:mask_gen_logits']}), discretized into binary masks using the Gumbel softmax with straight-through estimator (STE) (Eqs. \ref{['eq:mask_gen_gumbel']}–\ref{['eq:mask_gen_ste']}). (B) The selected temporal regions of the input are aggregated by integrating over the time dimension. (C) The aggregated features pass through a linear concept bottleneck layer with sparsity and orthogonality constraints. (D) Finally, a transparent linear prediction layer maps concept activations to the final output $\hat{y}$.
• Figure 2: Illustrative examples from the four synthetic TSER datasets. Regression targets are defined as areas under specific regions: above a fixed threshold (Univariate, Bivariate) or satisfying channel-wise inequalities (Trivariate-1, Trivariate-2). The Trivariate-2 target is a weighted sum of three conditional areas with coefficients $(A,B,C)=(1,5,-2)$.
• Figure 3: Concept bottleneck weights for a representative sample from the Univariate dataset. (a) Concepts learned without sparsity or orthogonality ($\lambda_{\mathrm{spars}},\lambda_{\mathrm{ortho}}=0$). (b) Concepts learned with both regularizers enabled ($\lambda_{\mathrm{spars}},\lambda_{\mathrm{ortho}}=1$). (c) Mapping from learned masks to the input signal, with ground-truth regions in green. (d) DeepLift attributions for the black-box CNN.
• Figure 4: Concept bottleneck weights for a representative sample from the Trivariate-2 dataset. (a) Concepts learned by MAGNETS ($\lambda_{\mathrm{spars}},\lambda_{\mathrm{ortho}}=1$). (b) Mapping from learned masks to the input signal, with ground-truth regions in green. Dim $i$ corresponds to the channel $i$ of the input time series. (c) DeepLift attributions for the black-box CNN.
• Figure 5: Concept bottleneck weights for a representative sample from the BridgeDegradation dataset. (a) Concepts learned by MAGNETS ($\lambda_{\mathrm{spars}},\lambda_{\mathrm{ortho}}=1$). (b) Mapping from learned masks to the input signal, with red arrows showing important masks. Dim $i$ corresponds to the channel $i$ of the input time series. (c) DeepLift attributions for the black-box CNN.