Graph Laplacian Wavelet Transformer via Learnable Spectral Decomposition

We introduce the Graph W avelet Transformer (GWT), a novel architecture that replaces this bottleneck with a learnable, multi-scale wavelet transform defined over an explicit graph Laplacian derived from syntactic or semantic parses. By parameterizing K N bandpass filters in the graph Fourier domain, GWT achieves a linear-time mixing operator that simultaneously captures local syntactic dependencies and global semantic context. We provide a rigorous mathematical formulation of the spectral filtering and mixing process, integrate GWT modules into a standard Graph Transformer backbone, and evaluate on the WMT14 English-German translation benchmark. Empirical results demonstrate that GWT outperforms the baseline Graph Transformer by 0.8 BLEU, reduces parameter count by 7 %, and speeds up inference by 15 %. Our analysis shows that multi-scale spectral decomposition offers an interpretable, efficient, and expressive alternative to quadratic self-attention for graph-structured sequence modeling.