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Abstract
En 中文
Graph neural networks are usually trained by gradient descent, with the graph serving as a fixed input rather than an active participant in optimization. We propose EFSA, an evolutionary framework with structural awareness that injects spectral properties of the graph—its normalized Laplacian, low-frequency eigenvectors, and derived topological descriptors—into all three pillars of an evolutionary optimizer. The fitness augments the task loss with a Dirichlet-energy penalty rewarding structurally smooth representations; topology-aware selection preserves structurally diverse candidates, weighting nodes by a centrality descriptor; and spectral mutation perturbs the node-latent block only within the K lowest-frequency eigenmodes, so that the block is parameterized by K×d0 spectral coefficients rather than by N×d0 free entries. Theoretically, we prove Lipschitz continuity of the structure-informed fitness, quantify the Dirichlet energy injected by spectral versus isotropic mutation, and establish, under an explicit local drift condition, an O(1/T) bound on the expected optimality gap of the best-so-far individual, where convergence is to a restricted optimum over the region reachable under the variation operators. A scale-balancing heuristic ties the regularization strength to the spectral gap, removing one hyperparameter. Across seven node-classification benchmarks spanning citation, co-authorship, and co-purchase networks, EFSA is competitive with strong gradient-based, graph-transformer, and architecture-search baselines, including capacity-matched baselines that receive the same spectral node-latent block and train it by gradient descent, with the largest gains on weakly connected graphs (small spectral gap), an exploratory trend consistent with the theory. We further report robustness under edge rewiring and ablations isolating the contribution of each structural component. The framework itself is formulated in a task-agnostic way, but the empirical evidence reported here is confined to transductive node classification, and our claims are scoped accordingly.
Journal
IF:
6.5
Papers:
2.5W
Citations:
6.5W
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