Neural Networks with Fractal Architecture

In this paper, we propose the Fractal Architecture Neural Network (FANN), a recursive neural framework inspired by self-similar fractal geometry. The architecture is governed by a fractal dimension parameter α, which controls the branching structure and connectivity density of the network, enabling multiscale feature representation through parameter sharing across recursive paths. We evaluate FANN on synthetic nonlinear regression tasks and compare it with a standard artificial neural network (ANN) and FractalNet in terms of accuracy, training behavior, and model complexity. Experimental results show that FANN achieves competitive or improved predictive performance under comparable computational budgets, demonstrating effective accuracy-to-parameter efficiency. These results suggest that fractal-inspired recursive connectivity can provide a compact mechanism for hierarchical representation learning in neural networks.