RhyMix: A Lightweight Adaptive Multi-Rhythm Network for Long-Term Time Series Forecasting

Real-world time series exhibit complex dynamics characterized by multiple simultaneous temporal patterns: short-term fluctuations, periodic seasonal cycles, long-term trends, and irregular abrupt changes. However, most forecasting architectures rely on single-path temporal modeling---transformers capture long-range dependencies but smooth local variations, convolutions capture local patterns but have limited receptive fields, and linear models are efficient but cannot capture nonlinear dynamics---so no single architectural paradigm captures all these pattern types simultaneously. To address this, we introduce RhyMix (RHYthm MIXture), a hybrid neural architecture designed around a parallel dual-path modeling paradigm with adaptive gating mechanisms. RhyMix integrates two complementary encoding branches: (i) a Cyclic Path that incorporates explicit seasonal inductive bias through learnable cyclic embeddings; and (ii) a lightweight Multi-Scale Temporal Convolutional Network with Channel Attention (MSTCN-CA) Path that captures temporal dependencies across different receptive fields. Unlike prior hybrid architectures that combine components with fixed weights, RhyMix computes its fusion weights from the input, adapting to each sample. Its key methodological contribution is a two-level adaptive gating framework: a per-channel path gate that fuses four specialized forecasting heads, and a per-sample hybrid gate that balances the two paths. This design maintains linear complexity. Across 12 real-world benchmarks, RhyMix achieves the best average MSE on 9 datasets and the best average MAE on 8 datasets. The model remains lightweight (40K parameters for C=7) with low-latency inference (5.2--7.5 ms), making it suitable for resource-constrained edge devices and real-time deployment.