Polynomial Precision Dependence Solutions to Alignment Research Center
  Matrix Completion Problems
Rico Angell
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.