Neural layers as stationary Schrödinger dynamics on latent graphs are shown equivalent to global supra-graph stationary systems, with coinciding hypothesis classes under strong-monotonicity assumptions and complexity bounds from graph geometry.
Consider the extended system d dtΦ(t, ψ0) = F (Φ(t, ψ0)), Φ(0, ψ0) = ψ0, where the right-hand side F ∈ C ∞
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Learning Latent Graph Geometry via Fixed-Point Schr\"odinger-Type Activation: A Theoretical Study
Neural layers as stationary Schrödinger dynamics on latent graphs are shown equivalent to global supra-graph stationary systems, with coinciding hypothesis classes under strong-monotonicity assumptions and complexity bounds from graph geometry.