Regularity3DGS: interpretable 3D Gaussian splatting via regularity-driven closed-loop optimization

3D Gaussian Splatting (3DGS) has become a powerful representation for high-fidelity and efficient neural 3D reconstruction. However, its optimization process remains largely opaque: Gaussian primitives are densified, pruned, and adjusted according to local numerical signals, while the long-term structural reasons behind these changes are rarely exposed or reused. As a result, redundant structures, unstable anchors, and geometry artifacts may emerge without an interpretable mechanism for diagnosis or correction. We propose Regularity3DGS, an interpretable regularity-driven framework that turns the hidden evolution of Gaussian primitives into explicit structural regularities and feeds them back into optimization. Regularity3DGS models long-term anchor behaviors across views and training iterations, identifies recurring scene-specific structural states, and maintains their reliability and lifecycle information in a dynamic structural regularity memory. The retained regularities are further transformed into continuous corrective signals to guide densification, pruning, and regularization, forming a closed optimization loop between structural interpretation and model update. Experiments show that Regularity3DGS provides explicit and traceable structural descriptions aligned with geometric evolution while maintaining competitive reconstruction performance. Importantly, contrary to the common belief that interpretability comes at the cost of performance, our approach achieves interpretability while further improving rendering quality, unifying high-performance neural rendering with self-interpretability.