Training 3D Spatially Embedded Neural Networks for Regression via Gradient Descent

This study examines a feed-forward neural network embedded in Euclidean R3 space. Nuclei coordinates condition network parameters. Backpropagating from loss-parameter to loss-coordinate derivatives enables spatially-embedded gradient descent. A dense multi-layer perceptron (MLP) learns price-prediction on the California Housing dataset. The model demonstrates performance comparable to conventional, non-spatial MLP predictions. Robustness examinations via re-initialisation sensitivity tests, and spatial analysis via node ablation and activation imaging, reveal complexity and interpretability characteristics unique to the spatially embedded model.