I think you do misunderstand. They do not add “correlated variables” to a model. The idea is that if you have an overparameterised model for a specific problem, this model contains a smaller model, that has similar performance to the trained large model, without training! That means gradient descent is in fact equivalent to pruning weights in a random network. There is no algorithm for how to do this efficiently (as they show) but that does not mean that there are no (so far unknown) heuristics out there that would get you close. This is exciting as it means a potential alternative for backprop is out there. This would be cool because it might mean more efficient algorithms and something I haven’t seen mentioned in the paper, an alternative to backprop that might be easier to understand in a biologically plausible way.