A Spectral Theory of Distortion in LLM Graph Reconstruction: Sharp Bounds and Empirical Characterization
The paper says a common spectral distortion score can hide whether an LLM copied, completed, or hallucinated a graph.
It proves sharp bounds for Wasserstein distance between Laplacian spectra using two edge-count summaries. The distance becomes especially blunt when a reconstruction only adds or only deletes edges, because it reduces to a scaled edge count. In mixed cases, the gap from the lower bound certifies that the model both lost real edges and invented new ones. The study tests 135 reconstructions from three open-weight models and finds differing editing policies that aggregate distortion alone would miss. ArXiv · AI/CL/LG's note
It proves sharp bounds for Wasserstein distance between Laplacian spectra using two edge-count summaries. The distance becomes especially blunt when a reconstruction only adds or only deletes edges, because it reduces to a scaled edge count. In mixed cases, the gap from the lower bound certifies that the model both lost real edges and invented new ones. The study tests 135 reconstructions from three open-weight models and finds differing editing policies that aggregate distortion alone would miss. ArXiv · AI/CL/LG's note
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