Breaking the 1-WL Barrier: Turbo Fiedler Deck as a Spectral Positional Encoding for Industrial-Scale GNNs
Pirolo Andres Sebastian · Zenodo (CERN European Organization for Nuclear Research) · 2025
Abstract ...We introduce the Turbo Fiedler Deck, a spectral-topological invariant that unifies combinatorial vertex criticality with Fiedler eigenvalue perturbation. Our method computes a permutation-invariant signature in polynomial time (O(n^3)) while O(n!) exact algorithms collapse under symmetry. The distinction is absolute: on the SRG(96) benchmark—a notorious "graveyard" for solvers—and adversarial CFI graphs, our method achieves 100% discrimination where standard GNNs fail deterministically. Theoretical Context This work directly addresses the "Expressivity Crisis" in geometric deep learning, fundamentally resolving the limitations identified in the seminal work of Xu et al. (ICLR 2019) regarding the blindness of message-passing architectures. By operationalizing the Kelly-Ulam Reconstruction Conjecture (1941) through the lens of Spectral Graph Theory, we demonstrate that the "1-WL Barrier" is not an endpoint, but a hurdle that can be vaulted via deterministic spectral physics. Key Contributions: 100% Accuracy on Adversarial Cases: Solves Cai-Fürer-Immerman (CFI) graphs and Strongly Regular Graphs (SRG). Industrial Scalability: Processed 31,364 USPTO molecules at 228 structures/second on a standard CPU (12GB RAM, No GPU). New Paradigm: Proposes a deterministic "Spectral Positional Encoding" to replace unstable Laplacian eigenvectors in Graph Transformers. Feedback and contact: [email protected] GitHub Repository: https://github.com/andydevok/TurboFiedlerDeck (Under construction - Code release pending publication, 21/12/25).