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I am looking for a way to implement a simple, 3-layer-25-neurons-per-layer neural net for an university essay (curve-fitting). What I see out there are the use of GPUs for dealing with huge Deep Neural Nets for computer vision and other applications. That seems like an overkill for my case.

What should I consider when implementing small nets for very simple problems?

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A small network for a simple problem should work perfectly fine on a standard home computer/laptop/whatever. The TensorFlow word2vec and MNIST demonstrations are perfectly reasonable on a consumer computer manufactured in the past few years.

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