On the Computational Power of Online Gradient Descent

3 Jul 2018  ·  Vaggos Chatziafratis, Tim Roughgarden, Joshua R. Wang ·

We prove that the evolution of weight vectors in online gradient descent can encode arbitrary polynomial-space computations, even in very simple learning settings. Our results imply that, under weak complexity-theoretic assumptions, it is impossible to reason efficiently about the fine-grained behavior of online gradient descent...

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