A Mixed Integer Linear Programming Formulation to Artificial Neural Networks

This paper studies the problem of computing an input vector for a given pair of Artificial Neural Network (ANN) and output vector, which is a kind of inverse problem. This problem has potential applications in design of new objects, especially in design of new chemical compounds. This paper focuses on ANNs in which activation functions are represented as continuous piece-wise linear functions, which can exactly represent ReLU functions and well approximate sigmoid functions. It is shown that this inverse problem can be formulated as a Mixed Integer Linear Programming Problem (MILP) with O(vertical bar V vertical bar + n(b) variables and constraints, where V is a set of neurons in a given ANN and nb denotes the total number of break points over all activation functions f(nu), nu is an element of V .