Analysis of Converged 3D Gaussian Splatting Solutions: Density Effects and Prediction Limits

We investigate what structure emerges in 3D Gaussian Splatting (3DGS) solutions from standard multi-view optimization. We term these Rendering-Optimal References (RORs) and analyze their statistical properties, revealing stable patterns-log-normal scales and bimodal radiance-across diverse scenes. To understand what determines these parameters, we apply learnability probes: training predictors to reconstruct RORs from point clouds without rendering supervision. Our analysis uncovers fundamental density-stratification: dense regions exhibit geometry-correlated parameters amenable to render-free prediction, while sparse regions show systematic failure across architectures. We formalize this through variance decomposition, demonstrating that visibility heterogeneity creates covariance-dominated coupling between geometric and appearance parameters in sparse regions. This reveals RORs' dual character-geometric primitives where point clouds suffice, view synthesis primitives where multi-view constraints are essential. We provide density-aware strategies that improve training robustness and discuss architectural implications for systems that adaptively balance feed-forward prediction and rendering-based refinement.