Reciprocity Can Erase Direction:tructural Boundaries and Controlled Utility of Magnetic Graph Networks

arXiv:2611.04295v1 Announce Type: new Abstract: Magnetic graph networks encode direction through phase, but a learned graph can erase the intended directional mechanism before prediction. We characterize this failure for support-based magnetic Laplacians. Exact identities relate imaginary energy and distance from zero phase to amplitude-weighted reciprocity. Top-$k$ selection forces complete collapse when the observed-node count satisfies $m\leq k+1$, and dense support imposes a lower bound on reciprocal-arc fraction. We then construct paired propagation examples with identical node features and symmetric amplitudes but opposite labels, giving a provable chance-level limit for direction-erasing representations. In 72 fixed neural fits, support phase achieved test AUROC 1.0000 on a unilateral ring but 0.5000 on reciprocal ring and complete supports; continuous score phase and a real directed comparator achieved 1.0000 throughout. All models solved the direction-free control. These are oracle-direction mechanism tests, not evidence of learned clinical direction. In the preserved public DeepDRiD development study, continuous phase was active but its robustness difference from zero phase was only $+0.0036$ (descriptive 95\% interval $-0.0014$ to $+0.0095$) on validation patients used for checkpoint selection. The contribution is a structural and experimental framework for distinguishing erased direction from unestablished task utility. It provides a precise circumstance in which magnetic phase preserves useful information, without asserting universal or clinical superiority.

Abstract:Magnetic graph networks encode direction through phase, but a learned graph can erase the intended directional mechanism before prediction. We characterize this failure for support-based magnetic Laplacians. Exact identities relate imaginary energy and distance from zero phase to amplitude-weighted reciprocity. Top-$k$ selection forces complete collapse when the observed-node count satisfies $m\leq k+1$, and dense support imposes a lower bound on reciprocal-arc fraction. We then construct paired propagation examples with identical node features and symmetric amplitudes but opposite labels, giving a provable chance-level limit for direction-erasing representations. In 72 fixed neural fits, support phase achieved test AUROC 1.0000 on a unilateral ring but 0.5000 on reciprocal ring and complete supports; continuous score phase and a real directed comparator achieved 1.0000 throughout. All models solved the direction-free control. These are oracle-direction mechanism tests, not evidence of learned clinical direction. In the preserved public DeepDRiD development study, continuous phase was active but its robustness difference from zero phase was only $+0.0036$ (descriptive 95\% interval $-0.0014$ to $+0.0095$) on validation patients used for checkpoint selection. The contribution is a structural and experimental framework for distinguishing erased direction from unestablished task utility. It provides a precise circumstance in which magnetic phase preserves useful information, without asserting universal or clinical superiority.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2611.04295 [cs.LG]

(or arXiv:2611.04295v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2611.04295 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Reciprocity Can Erase Direction:tructural Boundaries and Controlled Utility of Magnetic Graph Networks

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