Title: Joint Multi-Scale Forecasting with FFT and Gumbel Sampling
Primary area: learning on time series and dynamical systems
Keywords: Multi-scale decomposition; Fast Fourier Transform; Joint input-output representation

Abstract: Multi-scale decomposition has become a mainstream paradigm for time series forecasting. However, existing approaches primarily rely on the input sequence for scale separation, which introduces bias and limits predictive accuracy. In this work, we propose a novel forecasting framework that jointly leverages both input and output sequences to construct a more faithful multi-scale representation. At its core, an FFT-driven adaptive period selection module, augmented with Gumbel sampling, dynamically identifies dominant temporal scales while enabling stochastic yet structured scale exploration during training. To further improve stability and long-horizon robustness, we introduce an adaptive temperature gating mechanism that refines decoder initialization. Extensive experiments on multiple real-world benchmarks demonstrate that our method outperforms state-of-the-art models, providing new insights into temporal decomposition for time series forecasting.