Polynomial Precision Dependence Solutions to Alignment Research Center Matrix Completion Problems
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Abstract (arXiv)
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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References · 4
- 2017Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Datacited by 23
- 2021Optimal Convergence Rates for the Proximal Bundle Methodcited by 9
- 2022Formalizing the presumption of independencecited by 8
- 2020Revisiting Spectral Bundle Methods: Primal-dual (Sub)linear Convergence Ratescited by 5
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