[joe_the_user]

Well,

It's not just training that implies utility maximization, basic internal processes of a neural network, such as back propagation, are based on the utility function maximization. Back propagation is an approach that allows the network to do gradient descent on a utility function by propagating errors through the system.[1] Back propagation has been the way that deep networks have become tunable and effective. Without a utility function, it's hard to see how one would tune them.

And it's hard to think of what "mean maximization" could be but maximizing a utility function based on meaning.

And while you can construct a neural network that learns from a single example, the nn framework is fundamentally based on learning from multiple examples so such a construct is mostly meaningless.

But the point about machine learning being limited by the training methodology is good, it's just I'm pretty sure you'd different algorithms if you used a different methodology, the existing algorithms are used specifically because they fit the methodology.

[1]https://en.wikipedia.org/wiki/Backpropagation