The accepted answer does not answer the question
Why, if the above is correct, do we not see many neural network architectures projecting the data into higher dimensions first then reducing the size of each layer thereafter?
Yes, it's true that if you increase the number of hidden neurons, you generally increase the capacity (in fact, the VC dimension of ...
The accepted answer does not provide a good definition of over-fitting, which actually exists and is a defined concept in reinforcement learning too. For example, the paper Quantifying Generalization in Reinforcement Learning completely focuses on this issue. Let me give you more details.
Over-fitting in supervised learning
In supervised learning (SL), over-...
To better understand this you should think in terms of capacity. Capacity is a theoretical notion that shows how much information your network can model.
The capacity of a network (given sufficient training) ties in directly with the bias/variance tradeoff:
too little capacity and your network isn't able to learn the complex relationships in the data.
It's basically not possible to test besides some empirical experiments. All the generalization bounds only apply if your process actually follows the model assumptions which you don't actually know to be true.