Deterministic Spiral Sparsity as a Geometric Prior for Sparse Neural Networks

This paper studies deterministic spiral sparsity, a structured sparsity prior generated by mapping points from a Fermat spiral onto a weight matrix before training begins. Unlike unstructured pruning or random sparse initialization, the proposed approach uses a simple geometric rule to define which weights are trainable. We present the construction of the mask using the golden angle and report multi-seed studies on MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100. Our findings show that: MNIST 2% Density: The golden-angle mask dramatically outperforms matched random baselines by 12.6 percentage points, proving especially valuable at the extreme "edge" of sparsity. Generalization: While competitive overall, the advantage is dataset-dependent, with results on Fashion-MNIST and CIFAR being more mixed. Mechanism: Ablations suggest the useful property is structured, non-repeating connectivity geometry rather than the golden ratio alone. The contribution is best understood as a promising architectural prior that demonstrates how the spatial arrangement of fixed sparse connections can impact neural network performance.