> On the other hand, if a framework "correctly" implements the underlying statistical theory/principals of deep learning, shouldn't I get the same results regar

> On the other hand, if a framework "correctly" implements the underlying statistical theory/principals of deep learning, shouldn't I get the same results regardless of whichever framework I use? That is about right provided that 1) you use the same initial values and hyper-parameters, and 2) you can implement the same network with all frameworks. Issue 2) is complicated. Some networks are easy to implement in one framework can be hard or even impossible in another framework. Here "hard" can mean two opposite things: lack of flexibility (which disallows you to construct a certain topology) or excessive flexibility in the framework (which takes too many steps and care to construct a topology). Which framework to use depends on your goal and skill level. For starters, keras is usually easier.