Inprior work, ithas been shown that, when the constraints on the factorized variable regularly define a smooth manifold, providedk is large enough, for almost all cost matrices, all second-order stationary points (SOSPs) are optimal. Importantly, in practice, one can only compute points which approximately satisfy necessary optimality conditions, leading tothequestion: aresuch points also approximately optimal?

We prove that the ELBO is bounded, and the EM algorithm contributes to the convergence of ELBO.

This paper concerns the structure of learned representations in text-guided generative models, focusing on score-based models.

Neural Information Processing Systems http://nips.cc/

We consider the problem of minimizing a continuous function given given access to a natural quantum generalization of a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension versus accuracy trade-off which is provably unachievable classically and we prove that one method is asymptotically optimal in low-dimensional settings. Additionally, we provide quantum algorithms for computing a critical point of a smooth non-convex function at rates not known to be achievable classically. To obtain these results we build upon the quantum multivariate mean estimation result of Cornelissen et al. [25] and provide a general quantum variance reduction technique of independent interest.

Neural Information Processing Systems http://nips.cc/