Are there any guidelines reagarding the sampling process and the sample size?
For inititation of the new research or the project taken for the first time, small sample size can be taken. Usually sample size is determined on the basis of previous research. We calculate power of the study , then derive the sample size. What exactly you are planning to study regarding neural network?
The general answer would be that it depends on the complexity and nature of the problem, no. of classes and features involved, and the possible noise in the data.
To theoretically establish the minimum no. of samples required for training, you may take a look into the PAC (Probably Approximately Correct) framework.
There are many references out there for PAC that are a little 'fuzzy' to understand but I found these slides in the link below quite useful.
http://mi.eng.cam.ac.uk/~cz277/doc/Slides-PAC.pdf
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