Adaptive Oscillatory-State Alignment for Time Series Forecasting

Real-world time series are often governed by recurring patterns, but their dominant periods may vary across datasets, forecasting settings, and individual input windows. Existing cycle-aware forecasters commonly rely on a single period selected at the dataset level, which can be restrictive when periodic behavior changes over time or when multiple cycles coexist. Moreover, patch-based models typically process all patch positions uni- formly, although patches farther from the forecast boundary may require broader contextual refinement, while recent patches contain information that should be preserved more directly. Af- ter cyclic behavior is removed, the remaining dynamics may also span multiple temporal resolutions and cannot be adequately de- scribed at a single scale. We introduce CAMP, a Cycle-Aware Multi-Scale Patch Mixer designed to address these challenges. The Adaptive Cycle Learning module identifies dominant fre- quencies separately for each input window and generates both historical and future cyclic components without requiring a pre- defined cycle length. The Horizon-Guided Patch Mixer intro- duces position-dependent refinement, allowing earlier patches to incorporate broader temporal context while preserving infor- mation close to the forecast boundary. CAMP further models the de-cycled residual through temporally aligned multi-resolution representations, enabling complementary dynamics at different scales to be captured within one forecasting framework. Across seven long-term forecasting benchmarks, CAMP achieves the best average MSE on six datasets and the best or tied-best MAE on six. It also obtains the highest MSE win count across sixteen settings on four PEMS traffic benchmarks.

Accurate and efficient long-term multivariate time series forecasting requires capturing recurring temporal structure while keeping inference cheap across many variables and horizons. Frequency-space models represent long-range and periodic variation compactly, but they typically process the real and imaginary spectral components as weakly coupled streams and treat periodic cues as ordinary input features, even when such cues are unreliable. This paper proposes FRWKV-Plus, a lightweight periodic-aware frequency-space forecasting model built on the efficient FRWKV backbone. FRWKV-Plus introduces a cross-branch spectral gate that reweights each spectral branch using a summary of its sibling branch, and a trust-gated residual correction that converts compact within-period context into a bounded, sign-flexible adjustment of these gates under a learned, data-dependent trust score. By construction, the correction is identity-preserving at initialization and strictly bounded, so periodic evidence can refine but never dominate or invert the base interaction. On seven standard benchmarks, FRWKV-Plus is consistently competitive with strong linear, frequency-domain, recurrent-style, and Transformer-based forecasters while preserving the lightweight profile of the backbone. Controlled three-seed ablations show that each component contributes, that the benefit is modest on strongly periodic data and pronounced on the harder Exchange and ILI datasets, and that the within-period context is the most influential single component. The implementation is publicly available at https://github.com/yangqingyuan-byte/FRWKV-plus.

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, many existing 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. 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, capturing predictable rhythmic patterns; and (ii) a lightweight Multi-Scale Temporal Convolutional Network with Channel Attention Path that employs multi-scale depthwise dilated convolutions to capture temporal dependencies across different receptive fields. A key innovation is the use of adaptive gating at multiple levels: a path gate dynamically combines four specialized forecasting heads (Direct, Trend-Seasonal Decomposition, Local Convolution, and Periodic Fusion) per sample and channel, while a hybrid gate adaptively balances the Cyclic and MSTCN-CA Paths based on input characteristics. This design ensures the model adapts to specific temporal patterns while maintaining linear complexity in sequence length, channels, and prediction horizon. Across extensive benchmarks on 12 real-world datasets for long-term forecasting, RhyMix achieves state-of-the-art performance on 10 of 12 datasets. The model remains lightweight (~40K params) with linear complexity and low-latency inference (<5ms),suitable for resource-constrained edge devices and real-time deployment.