The analysis of Multivariate Time Series (MTS) plays an important role in a lot of real-world practical applications, but it still remains some challenging problem about capturing multi-granularity structural patterns and suppressing noise appropriately. Multi-Scale Convolution with Optimal Transport Attention (MSC-OT) is proposed in this paper. MSC-OT is a useful architecture to optimize the attention mechanism. It combines multi-scale convolution with Sinkhorn optimal transport method based on inverted embedding. The inverted embedding approach embeds each variable as a token and allows the model to capture cross-variate relationships better. MSC-OT consists of two part: (1) Multi-Scale Convolution Enhancement, that applies multi-scale convolutions to attention score matrices based on inverted embedding, capturing local structural patterns in the variate-interaction space induced by compressed temporal representations; (2) Sinkhorn Optimal Transport Regularization, that formulates attention computation as an optimal transport problem and employs iterative matrix scaling to ensure balanced information flow across variates. Adaptive Fusion Strategy utilizes softmax-normalized learnable weights to dynamically combine base attention, convolution-enhanced, and OT-regularized scores. Experiments on widely-used datasets, including ETT, Electricity, Traffic, Solar-Energy, and Exchange-Rate, show that MSC-OT achieves well performance in both short-term and long-term forecasting tasks. Ablation experiments further validate the effectiveness of each proposed component and their synergistic contributions to improving prediction accuracy for multivariate 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.