AnchorMoE: Interpretable Time Series Classification via Anchor-Routed MoE

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.

Time Series Classification (TSC) is a long-standing research problem that has gained increasing attention in recent years with the rapid growth of large-scale temporal data. Despite substantial progress enabled by deep learning, designing TSC models that are both accurate and interpretable remains a challenging task. Many existing approaches adopt a direct feature-to-label classification paradigm, by collapsing high-dimensional temporal embeddings into class logits via a single linear projection (often after global pooling), the paradigm conflates feature extraction and decision logic into an inseparable mapping. To address these limitations, we propose PDFTime, a prototype-guided framework that reformulates time series classification as a multi-stage decision process. Instead of direct feature-to-label mapping, PDFTime leverages learned prototypes to approximate class-conditional feature distributions in the latent space, enabling progressive discrimination through classification sub-tasks of varying granularity. To our knowledge, PDFTime is the first framework to reformulate time series classification as a decoupled, multi-stage similarity-based reasoning process, breaking the long-standing paradigm of direct, black-box feature-to-label mapping. Extensive evaluations demonstrate that PDFTime achieves state-of-the-art (SOTA) performance across UEA and UCR benchmarks. Notably, it secures the top-$1$ accuracy on 80 out of 128 datasets in the UCR archive, significantly outperforming recent strong baselines in both consistency and generalization.

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. The code implementation and datasets are publicly available at https://github.com/FlorentF9/MAGNETS.