The real 'knowledge' or the learning that makes a neural network give results is the values behind of the edge weights which are literal expressions (numbers) as seen below. The neural network is essentially useless without these appropriate values and hence this is an extremely valuable intellectual property. Is copy-right protection available for this? What all elements of a neural network get IP protection?
Do the weights of a neural network get any kind of IP protection?
Almost certainly not, as they are obvious (in a patent sense). The reasoning for this is a little bit indirect.
Neural networks in general are very well-known and commonplace. In addition, training methods for neural networks are very well-known. By applying a known training method to a known neural network, you are doing nothing more than what has been done thousands of times before. The fact that you have a unique series of values as an output is not in itself non-obvious, since they were obtained by well-known and obvious techniques. As such, it would be obvious for the person skilled in the art to try the same approach, and they would then obtain substantially the same results.
Unless you have invented a unique type of neural network, or a unique method for training, or a unique step of filtering data, or the neural network is being applied in a suprising area, then you're really doing nothing non-obvious.
Copyright is off-topic here, and I would encourage you to post a similar question on Law.SE to get a full answer.
However, as an aside, almost certainly there would be no copyright in the weights of a neural network, since they would not involve even a modicum of creativity.