On the Computational Power of Online Gradient Descent

On the Computational Power of Online Gradient Descent

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 behav...

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Hauptverfasser: Chatziafratis, Vaggos, Roughgarden, Tim, Wang, Joshua R
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science - Learning
Statistics - Machine Learning
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Zusammenfassung: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.
DOI:10.48550/arxiv.1807.01280