Tonnetz-Driven Graph Wedgelet for Harmonic Complexity Reduction in Music Scores

What the math gives to ML

The paper supplies a constructive, graph-geometric compression mechanism: recursively partition a connected graph by two-seed shortest-path Voronoi wedges, then replace each region by its mean signal. The transferable asset is not the music-specific Tonnetz embedding itself, but the combination of connectivity-preserving binary partitioning, adaptive split selection, and an explicit least-squares approximation error. This can become a graph-token pooling layer for graph transformers or structured symbolic-music models, reducing the number of nodes while keeping nearby, task-similar nodes together. The most direct test is to compare this wedge pooling against random pooling, k-means pooling, and attention-based token merging at equal retained-token budgets.