A new method is developed to determine a set of informative and refined interface assertions satisfied by functions that are represented by feed-forward neural networks. Neural networks have often been criticized for their low degree of comprehensibility.It is difficult to have confidence in software components if they have no clear and valid interface description. Precise and understandable interface assertions for a neural network based software component are required for safety critical applications and for theintegration into larger software systems. The interface assertions we are considering are of the form &quote if the input x of the neural network is in a region (alpha symbol) of the input space then the output f(x) of the neural network will be in the region (beta symbol) of the output space &quote and vice versa. We are interested in computing refined interface assertions, which can be viewed as the computation of the strongest pre- and postconditions a feed-forward neural network fulfills. Unions ofpolyhedra (polyhedra are the generalization of convex polygons in higher dimensional spaces) are well suited for describing arbitrary regions of higher dimensional vector spaces. Additionally, polyhedra are closed under affine transformations. Given a feed-forward neural network, our method produces an annotated neural network, where each layer is annotated with a set of valid linear inequality predicates. The main challenges for the computation of these assertions is to compute the solution of a non-linear optimization problem and the projection of a polyhedron onto a lower-dimensional subspace.