Frequency-Guided Deformable Networks for Continuous Phase Alignment

The core of time series analysis lies in effectively modeling the physical laws within complex signals. Existing Transformer and Convolution Neural Network (CNN) architectures are often constrained by insufficient temporal inductive bias, restricted frequency extraction capabilities, or weak local phase alignment. To this end, this paper proposes Adaptive Network Based on Cascaded Harmonic Offset Routing (ANCHOR), an Adaptive Network based on Cascaded Harmonic Offset Routing. The model utilizes the Real Fast Fourier Transform (RFFT) to extract explicit dominant periods, injecting them as physical anchors into the dilation operators of multi-branch deformable convolutions. This guides the adaptive optimization of sampling locations in the time domain, achieving synergistic modeling of macroscopic periodic priors and microscopic geometric deformations. Furthermore, to address the quantization errors and picket-fence effects introduced by the discrete RFFT, this paper imports a continuously differentiable 1D Gaussian Radial Basis Function interpolation operator to replace traditional linear interpolation. This maintains the differentiability of the interpolation process and enhances the accuracy of sub-pixel phase compensation. Additionally, ANCHOR introduces an asymmetric routing mechanism and orthogonal channel partitioning to dynamically balance the extraction weights between high-energy strong signals and low-energy weak features. Multi-task benchmark experiments demonstrate that ANCHOR achieves the best or solid performance in short-term forecasting, anomaly detection, and time series classification tasks. Code is available at https://github.com/Jwy-EE/Anchor_pub