Explicit vs Implicit Representations: A Systematic Comparison of GA-Planes, K-Planes, and NeRF for 2D Matrix Reconstruction

Keywords: K-planes, GA-planes, NERF, matrix reconstruction

Abstract: Implicit Neural Representations (INRs) have shown remarkable success in 3D scene reconstruction, but their effectiveness for 2D matrix reconstruction remains underexplored. We present the first systematic comparison of INR architectures—GA-Planes, K-Planes (a subset of GA-Planes), and NeRF variants—adapted for 2D matrix reconstruction tasks. Our comprehensive evaluation across 360 experiments demonstrates that the best GA-Planes configuration achieves 27.67±2.61 dB PSNR, while K-Planes (multiply, nonconvex) achieves 27.43±2.42 dB, both substantially outperforming NeRF's best result of 12.41±0.41 dB by over 15 dB. This represents compelling evidence that explicit geometric factorization outperforms implicit coordinate encoding for 2D domains. We establish critical design principles: multiplicative feature combination outperforms additive approaches, and nonconvex decoders provide significant benefits over linear decoders. Our fair comparison methodology with parameter matching isolates architectural effects from model capacity, providing rigorous evidence for design choices in neural representations.

Submission Number: 234