MoHETS: Long-term Time Series Forecasting with Mixture-of-Heterogeneous-Experts

Real-world multivariate time series can exhibit intricate multi-scale structures, including global trends, local periodicities, and non-stationary regimes, which makes long-horizon forecasting challenging. Although sparse Mixture-of-Experts (MoE) approaches improve scalability and specialization, they typically rely on homogeneous MLP experts that poorly capture the diverse temporal dynamics of time series data. We address these limitations with MoHETS, an encoder-only Transformer that integrates sparse Mixture-of-Heterogeneous-Experts (MoHE) layers. MoHE routes temporal patches to a small subset of expert networks, combining a shared depthwise-convolution expert for sequence-level continuity with routed Fourier-based experts for patch-level periodic structures. MoHETS further improves robustness to non-stationary dynamics by incorporating exogenous information via cross-attention over covariate patch embeddings. Finally, we replace parameter-heavy linear projection heads with a lightweight convolutional patch decoder, improving parameter efficiency, reducing training instability, and allowing a single model to generalize across arbitrary forecast horizons. We validate across seven multivariate benchmarks and multiple horizons, with MoHETS consistently achieving state-of-the-art performance, reducing the average MSE by $12\%$ compared to strong recent baselines, demonstrating effective heterogeneous specialization for long-term forecasting.

Seg-MoE: Multi-Resolution Segment-wise Mixture-of-Experts for Time Series Forecasting Transformers

Transformer-based models have recently made significant advances in accurate time-series forecasting, but even these architectures struggle to scale efficiently while capturing long-term temporal dynamics. Mixture-of-Experts (MoE) layers are a proven solution to scaling problems in natural language processing. However, existing MoE approaches for time-series forecasting rely on token-wise routing mechanisms, which may fail to exploit the natural locality and continuity of temporal data. In this work, we introduce Seg-MoE, a sparse MoE design that routes and processes contiguous time-step segments rather than making independent expert decisions. Token segments allow each expert to model intra-segment interactions directly, naturally aligning with inherent temporal patterns. We integrate Seg-MoE layers into a time-series Transformer and evaluate it on multiple multivariate long-term forecasting benchmarks. Seg-MoE consistently achieves state-of-the-art forecasting accuracy across almost all prediction horizons, outperforming both dense Transformers and prior token-wise MoE models. Comprehensive ablation studies confirm that segment-level routing is the key factor driving these gains. Our results show that aligning the MoE routing granularity with the inherent structure of time series provides a powerful, yet previously underexplored, inductive bias, opening new avenues for conditionally sparse architectures in sequential data modeling.

T-Explainer: A Model-Agnostic Explainability Framework Based on Gradients

The development of machine learning applications has increased significantly in recent years, motivated by the remarkable ability of learning-powered systems to discover and generalize intricate patterns hidden in massive datasets. Modern learning models, while powerful, often exhibit a level of complexity that renders them opaque black boxes, resulting in a notable lack of transparency that hinders our ability to decipher their decision-making processes. Opacity challenges the interpretability and practical application of machine learning, especially in critical domains where understanding the underlying reasons is essential for informed decision-making. Explainable Artificial Intelligence (XAI) rises to meet that challenge, unraveling the complexity of black boxes by providing elucidating explanations. Among the various XAI approaches, feature attribution/importance XAI stands out for its capacity to delineate the significance of input features in the prediction process. However, most existing attribution methods have limitations, such as instability, when divergent explanations may result from similar or even the same instance. In this work, we introduce T-Explainer, a novel local additive attribution explainer based on Taylor expansion endowed with desirable properties, such as local accuracy and consistency, while stable over multiple runs. We demonstrate T-Explainer's effectiveness through benchmark experiments with well-known attribution methods. In addition, T-Explainer is developed as a comprehensive XAI framework comprising quantitative metrics to assess and visualize attribution explanations.