Algebraic Complexity and Neurovariety of Linear Convolutional Networks

In this paper, we study linear convolutional networks with one-dimensional filters and arbitrary strides. The neuromanifold of such a network is a semialgebraic set, represented by a space of polynomials admitting specific factorizations. Introducing a recursive algorithm, we generate polynomial equations whose common zero locus corresponds to the Zariski closure of the corresponding neuromanifold. Furthermore, we explore the algebraic complexity of training these networks employing tools from metric algebraic geometry. Our findings reveal that the number of all complex critical …

algorithm complexity cs.lg filters generate linear math.ag network networks paper polynomial recursive set space study