CAMP: A Cycle-Aware Multi-Scale Patch Mixer for 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, 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.

Reliable periodic patterns serve as a fundamental basis for accurate multivariate time series forecasting. However, existing methods either implicitly extract periodicity through complex model architectures (e.g., Transformers) with high computational overhead or overlook the intrinsic phase-amplitude coupling when modeling periodic components explicitly. To address these issues, we propose a novel Cycle-aware Phase-Amplitude Modulation Network (PAMNet) that explicitly decomposes periodic patterns into complementary phase and amplitude components. The core innovation lies in its dual-branch modulator, featuring dedicated learnable embeddings for phase positioning and amplitude modulation. The phase branch employs cyclical embeddings to capture phase-dependent mean shifts, while the amplitude branch models intensity variations to adapt to changes in variance. A lightweight modulator with element-wise fusion efficiently combines these components, enabling explicit modeling of their interactions without complex attention mechanisms. Extensive experiments on twelve real-world datasets demonstrate that our method achieves state-of-the-art performance through its novel phase-amplitude decoupling mechanism, offering a new perspective for cyclical modeling in time series forecasting.

Multivariate time series forecasting remains a challenge due to the complexity of local temporal dynamics and global dependencies across multiple variables. In this paper, we propose \textbf{N}eighboring \textbf{P}atching \textbf{Mixer} (\textbf{NPMixer}), a hierarchical architecture featuring a Learnable Stationary Wavelet Transform that adaptively learns filter coefficients to decompose signals into trend and detail components in a data-dependent manner. Our framework introduces a Neighboring Mixer Block that captures local temporal dynamics through a series of hierarchical MLP layers operating on non-overlapping patches. Specifically, the mixer block utilizes MLPs to learn temporal patterns within and across these patches, expanding the receptive field to capture multi-scale dependencies. A Channel-Mixing Encoder is applied to high-frequency components to learn channel correlations while preserving the stability of the underlying global trend. Extensive experiments on seven benchmark datasets demonstrate that NPMixer consistently outperforms state-of-the-art models, achieving better performance in 20 out of 28 ($71.4\%$) evaluated experimental setups for MSE.