The idea is simple.
In machine learning you need to calculate the error depending on some parameters. To be able to optimize them.
Some simple cost function is the Mean Squared Error. https://en.wikipedia.org/wiki/Mean_squared_error
My idea is to see if one can use “similarity” of two objects instead. Like you visually compare two images and set a value on how similar they are. Here the objects could be two vectors.
One example could be two audio files that sound the same but are not matched sample for sample.
This could be the basis of a smart cost function. That is. You use machine learning to produce a cost function that outputs the similarity value.