Is it possible to do K-nearest-neighbours before training DNN The following X-shape alternated pattern can be separated quite well and super fast by K-nearest Neighbour algorithm (go to https://ml-playground.com to test it):

However, DNN seems to face great struggles to separate that X-shape alternated data. Is it possible to do K-nearest before DNN, ie. set the DNN weights somehow to simulate the result of K-nearest before doing DNN training?
Another place to test the X-shape alternated data: https://cs.stanford.edu/people/karpathy/convnetjs/demo/classify2d.html
There are two factors that will change the ability of a deep neural network to fit a given dataset: either you need more data, or a deeper and wider network. Since the pattern is only 2-d, it can likely be approximated by some sort of simple periodic function. A DNN can approximate periodic functions pretty well, so the issue is probably that you don't have enough data. 

If you have an apriori belief that the pattern is well approximated by K-nearest neighbors, then you could do the following:


Fit a K-NN model to the data.
Generate $N$ new points uniformly at random from the input space.
Label the $N$ new points using the K-NN model.
Fit your DNN to the original dataset, plus the $N$ new points.