So, "deep learning" is the idea of doing representation learning via a chain of learned feature extractors. It's all about describing some input data via *deep hierarchies of features*, where features are *learned*.
A further question is then: is the brain "deep learning"?
The only good answer here: the brain is an incredibly complex thing, encompassing many parts that are structured differently, and we know extremely little about it. We cannot definitely answer the question.
However, my gut feeling is that the brain is generally not DL, although some submodules could be described as DL or part-DL (e.g. the visual cortex is a deep hierarchy of features, albeit not all are learned, and has been a considerable source of inspiration in DL).
I would add that our current understanding and usage of modern deep learning -- its genealogy -- lies mostly in earlier modern machine learning techniques, not in neuroscience. The influence of neuroscience has been one of high-level conceptual inspiration, not direct emulation.
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