BeepBoop seems to be the new king

I’ve been meaning to release the code for the training, but it’s currently a huge mess and I’m pretty busy! In the meantime, here are some details that might help:
* I initialized the powers to 1, biases to 0, and multipliers to a simple hand-made KNN formula. 
* I constrained the powers to be positive, so I guess the formula should really be written as w(x+b)^abs(a). 
* I used Adam with a learning rate 1e-3 for optimization.
* Changing the KNN formula of course changes the nearest neighbors, so I alternated between training for a couple thousand steps and rebuilding the tree and making new examples.
* For simplicity/efficiency, I used binning to build a histogram over GFs for an observation. Simply normalizing the histogram so it sums to 1 to get an output distribution doesn’t work that well (for one thing, it can produce very low probabilities if the kernel width is small). Instead, I used the output distribution softmax(t * log(histogram + abs(b))) where t and b are learned parameters initialized to 1 and 1e-4.