Supplemental: Training Fully Connected Neural Networks is R-Complete A R-Membership Membership in R is already proven by Abrahamsen, Kleist and Miltzow in [

F or each line ℓ L the change of the gradient of f when crossing ℓ is constant along ℓ. Then there is a fully connected two-layer neural network with m hidden neurons computing f . To see that this observation is true, consider the following construction. Describing all gadgets purely by their data points is tedious and obscures the relatively simple geometry enforced by these data points. A weak data point relaxes a regular data point and prescribes only a lower bound on the value of the label.