Polynomial Precision Dependence Solutions to Alignment Research Center Matrix Completion Problems

• URL: http://arxiv.org/abs/2401.03999v1
• Date: Mon, 8 Jan 2024 16:25:45 GMT
• Title: Polynomial Precision Dependence Solutions to Alignment Research Center Matrix Completion Problems
• Authors: Rico Angell
• Abstract summary: The motivation for these problems is to enable efficient dependence on $varepsilon$. Our solutions involve reframing the matrix completion problems as a semidefinite program (SDP)
• Score: 3.796436257221663
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of heuristic estimators to formally evaluate and reason about different quantities of deep neural networks in the interest of AI alignment. Our solutions involve reframing the matrix completion problems as a semidefinite program (SDP) and using recent advances in spectral bundle methods for fast, efficient, and scalable SDP solving.

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