SPARCS (SPectral ARchiteCture Search) is a novel architecture search protocol for solving architecture design and optimization problems in artificial neural networks. It leverages the spectral properties of the interlayer transfer matrix to generate continuous and differentiable manifolds, enabling the use of gradient-based optimization algorithms. Using a simple benchmark model, we demonstrate that the proposed method generates self-emergent architectures with minimal expressive power and a reduced number of parameters compared to other feasible alternatives for the task under study.