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This paper identifies that standard ridge regularization in potential recovery from flow on directed graphs collapses and reverses the ordering of the estimate due to gauge dependence. It proposes a gauge-invariant Dirichlet energy penalty that yields a parameter-insensitive solution and demonstrates robust dynamic range preservation on real clickstream data, with implications for preventing oversmoothing in graph neural networks.
This paper proposes incorporating symmetries into affinity kernels for spectral embedding, proving convergence of invariant graph Laplacians on quotient manifolds with improved sample complexity.