One of the primary drivers of the success of machine learning methods in open-world perception settings, such ascomputer vision [19]and NLP [8],has been the ability ofhigh-capacity function approximators, suchasdeepneuralnetworks,tolearngeneralizable modelsfromlargeamountsof data.

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 is an idealization of the usual way to train neural networks with a large hidden layer.

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/

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

Recent progress in the development of voltage indicators [1-8] has brought us closer to a longstanding goal incellular neuroscience: imaging the full spatiotemporal voltageonadendritic tree. These recordings have the potential (pun not intended) to resolve fundamental questions about the computations performed by dendrites -- questions that have remained open for more than a century[9,10].