Aggregation is itself a spectral valley: SpecValley learns where the valley sits, leading four of six heterophilic graphs
In node classification on heterophilic graphs, the step before propagation has stayed fixed by degree normalisation, which acts spectrally as a valley whose zero is set by the normalisation rather than by the data, exactly where dense graphs' eigenvalues accumulate. SpecValley learns the valley's centre, sharpness and flank gains per graph, then feeds an ordinary ChebNet spectral filter. Across six heterophilic benchmarks it matches or exceeds the best published result on four, sits within the confidence interval of the best on Tolokers, and trails on Actor; crossing five aggregators with four filters attributes the gain to aggregation rather than to the downstream filter.