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OP-0049Deep learning theoryOpen

Depth separation for functions learnable by gradient descent

Depth-3 networks can express functions depth-2 cannot. Whether training can find them is a different question, and it is open.

Community consensus· 2016

OP-0047Deep learning theoryOpen

Characterise the implicit bias of gradient descent for non-linear networks

For linear models the answer is a clean minimum-norm statement. For anything deeper, there is no general theory.

Community consensus· 2017