A Spectral Theory of Distortion in LLM Graph Reconstruction: Sharp Bounds and Empirical Characterization
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 $n$
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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 $n$
This paper provides a rigorous mathematical framework for evaluating the fidelity of graph reconstruction by LLMs, moving beyond aggregate metrics. Understanding these sharp bounds helps ML engineers design more robust evaluation strategies and interpret LLM performance on graph-structured data tasks more accurately.