@JeffE yes, that is perhaps a better way of writing the sentence that I used as an example of how I normally cite articles. I edited my question, so hopefully it's easier to understand what I'm asking now.

@user2768 thanks for your reply, I am sorry I do not exactly understand your question. The thing is like this: CPU: Computations will be serial, and hence they will result in the same answer. GPU: Computations may be executed in different order, so results may differ. Also the architectures treats floating points differently. As I have understood, the GPU rounds floating points to a higher degree (now I am almost guessing)... But anyway, I don't want this topic to become too technical. I am mostly curious about the academic point of view and the "liability" of results.

@101010111100 to be specific, I am implementing a neural network model using Keras API which runs on top of TensorFlow which uses GPU acceleration. The exact reason for the randomness is maybe a bit off-topic in this question, and to be honest I do not exactly know the reason. There are many threads or topics on other websites where people discuss the problem, and the vanilla solutions such as seeding consistently won't work for anyone. Another solution is to switch backend to Theano which I am about to try out now. However, this is probably questions for some other stack-site..

@Saturnus you mean when presenting the results? The thing is that running on the CPU will probably take many hours, if not days. I could do a few runs, but as I have very many parameters to adjust, doing all combinations of parameter setups would not allow me to present a complete set of data for the CPU runs.. So basically I am asking if I will be "failed" for not showing the exact calculations. I know that is probably hard to answer as it is completely up to my examiner (this is a thesis work).. But besides my specific thesis case, I am still interesting in how these things usually are done.

That is a very good point you make, about the consistency of notation. This is one reason for me not to just reference to the book I have.. because I used other notations in preceding parts of my text. Thank you for making me aware of that!