Supplemental: TrainingFullyConnectedNeuralNetworksis R-Complete A R-Membership

Membership in Ris already proven by Abrahamsen, Kleist and Miltzow in [3]. Thealgorithm then needs to verify that the neural network described byΘ fits all data points inD with a total error at mostγ. The goal of this appendix is to build a geometric understanding off(,Θ). We point the interested reader to these articles [6, 26, 49, 66, 92] investigating the set of functions exactly represented by different architecturesofReLUnetworks. To see that this observation is true, consider the following construction.