Auto-Configured Networks for Multi-Scale Multi-Output Time-Series Forecasting

Hierarchical forecasting exploits aggregation structures that expose multiple views of the same underlying spatiotemporal forecasting problem, while ensuring coherence among forecasts. Individual series provide fine-grained information, while progressively coarser aggregates reveal temporal and spatial patterns at different scales. In the associated deep learning architectures, the hierarchy determines which aggregate series are available and how they are processed together with individual series (e.g., through reconciliation or message-passing operators). Different hierarchies thus provide distinct learning signals and inductive biases for forecasting the same collection of time series. Nonetheless, existing architectures are typically trained on a single, often fixed, structure. In this work, we propose a graph deep learning framework that leverages variations across hierarchies as multi-task regularization. We show that jointly learning across these structures can reduce over-specialization to any single hierarchy and improve forecasting performance. Indeed, training across hierarchies provides an inductive bias toward representations that are useful across different structures, and as such, generalize better. Making forecasts coherent with the aggregation constraints for each sampled hierarchy is computationally expensive: to complement the framework, we propose a novel operator-based on a top-down approach-that produces coherent forecasts with linear time and space complexity w.r.t. the hierarchy size. Experiments show that our approach improves forecasting accuracy over training on a single structure and is competitive with current state-of-the-art methods.

Time series forecasting is vital across many domains, yet existing models struggle with fixed-length inputs and inadequate multi-scale modeling. We propose MR-CDM, a framework combining hierarchical multi-resolution trend decomposition, an adaptive embedding mechanism for variable-length inputs, and a multi-scale conditional diffusion process. Evaluations on four real-world datasets demonstrate that MR-CDM significantly outperforms state-of-the-art baselines (e.g., CSDI, Informer), reducing MAE and RMSE by approximately 6-10 to a certain degree.

Multi-scale modeling has emerged as an effective design principle for time-series forecasting by capturing temporal dynamics at multiple resolutions. As no principled foundation has been established in the literature, we unify existing scaling methods into a scaling operator family, revealing a fundamental limitation of existing approaches: reliance on fixed and discrete scaling. To address this limitation, we propose SiGMA (Single Generalized Multi-scale Architecture), which enables distance-aware scaling via the learnable discrete Gaussian (LDG) kernel grounded in scale-space theory. We evaluate SiGMA comprehensively on long- and short-term forecasting benchmarks against state-of-the-art multi-scale baselines. SiGMA outperforms all competitors on both tasks, especially achieving the best performance in 13 out of 16 long-term evaluation settings. Beyond accuracy, SiGMA significantly improves training speed by up to 5.3 times and reduces memory consumption by up to 3.8 times over the strongest competitors. Code is available at https://github.com/cheonwoolee/SiGMA.