A Spectral Theory of Distortion in LLM Graph Reconstruction: Sharp Bounds and Empirical Characterization

תקציר מקורי באנגליתarXiv:2609.38161v1 Announce Type: new Abstract: Evaluations of graph reconstruction by language models typically report a single aggregate distance between the original and the reconstructed graph. We prove that for the Wasserstein distance between Laplacian spectra such a summary is bracketed by two edge counts, the net change in edge number from below and the symmetric difference from above, each scaled by $2/n$ where $n$ is the number of vertices. The bracket is sharp: its two ends coincide exactly when the reconstruction only adds edges or only deletes them, and on that class the distance is a rescaled edge count that says nothing about which edges changed. When the ends differ, the residual between the distance and the lower end is positive only if the reconstruction both invented and