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Multigrid methods are among the most effective preconditioners, yet their performance is dictated by the accurate construction of grid transfer operators. Current neural multigrid methods learn such operators with graph neural networks (GNNs), typically by extracting connectivity from discretized system matrices. While effective, these graph-based constructions suffer from rank inflation, resulting in unnecessarily large coarse spaces and slower convergence. To ameliorate, this paper advocates NeuraLSP, a new neural multigrid preconditioner that replaces graph aggregation with a fixed low-rank spectral representation derived from the left singular subspace of near-nullspace components. 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