Polynomial Precision Dependence Solutions to Alignment Research Center Matrix Completion Problems
This work addresses AI alignment by providing efficient tools for formal evaluation of deep neural networks, though it appears incremental as it applies existing methods to specific problems.
The authors tackled matrix completion problems from the Alignment Research Center by developing solutions with polynomial dependence on precision, enabling efficient computation of heuristic estimators for evaluating deep neural networks in AI alignment. They achieved this by reframing the problems as semidefinite programs and using spectral bundle methods for fast solving.
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.