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.
Step 1 dGH ((V, dG∗), G) ≤ C1δ: Since V is a δ-net in G and G∗ uses edges EG = {(u, v) : dG(u, v) < ρ/ 2}: - For any u, v ∈ V , dG∗(u, v) ≤ dG(u, v) + O(δ) (by triangle inequality)
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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.