Here's the thing. You said "deep learning is OLS with constructed regressors." Is it in the same family? Yes. No one's arguing that.
As someone who is a scientist who studies machine learning, I am telling you, specifically, in machine learning, no one calls deep learning OLS. If you want to be "specific" like you said, then you shouldn't either. They're not the same thing.
If you're saying "OLS family" you're referring to the overall task of supervised learning, which includes things from boosted trees to SVMs to non parametric regression.
So your reasoning for calling deep learning OLS is because random networks "end with a linear layer?" Let's get DSGEs and structural models and random forests yin there, then, too?
Also, calling someone a human or a horse?. It's not one or the other, that's not how economics works. They're both. Deep learning is deep learning and a member of the supervised learning family.1 But that's not what you said. You said deep learning is OLS, which is not true unless you're okay with calling all members of the supervised learning family OLS, which means you'd call SVMs, boosted trees, and other classification and regression frameworks OLS, too. Which you said you don't.
It's okay to just admit you're wrong, you know?
Other than deep RL (reinforcement learning), dark knowledge (semi supervised), GANs, autoencoders, or VAEs (unsupervised learning). But that would further disrupt the circlejerk.
