Inference networks oftraditional Variational Autoencoders (VAEs) aretypically amortized, resulting in relatively inaccurate posterior approximation compared to instance-wise variational optimization. Recent semi-amortized approaches were proposedtoaddress thisdrawback; however,theiriterativegradient update procedures can be computationally demanding.

The appendix consists of proofs (Section A), additional theoretical results (Section B), and numerical experiments (Section C). When g is strictly increasing, the mapping x7 g(x) is sign preserving. Specifically, if x 0, then g(x) g(0) = 0. Conversely, ifg(x) 0 = g(0), then applying g 1 to both sides givesx 0. When g is strictly decreasing, the mappingx7 g(x) is sign reversing. See Section B.2 for constructive examples. Based on the definition of classification lossL(,), the function Risk() relies only on the sign pattern of the tensor.

A nonparametric approach to tensor completion is developed based on anewmodel which we coin assign representable tensors. The model represents the signal tensor of interest using a series of structured sign tensors. Unlike earlier methods, the sign series representation effectively addresses both low-andhigh-rank signals, while encompassing manyexisting tensor models-- includingCPmodels,Tuckermodels,singleindexmodels,structuredtensorswith repeating entries--as special cases. We provably reduce the tensor estimation problem to a series of structured classification tasks, and we develop a learning reduction machinery to empower existing low-rank tensor algorithms for more challenging high-rank estimation.

RFK Jr. Says Americans Need More Protein. A 30-second Super Bowl ad featuring boxing legend Mike Tyson and paid for by the nonprofit MAHA Center encourages viewers to avoid processed foods and visit Realfood.gov . The government website, which Health and Human Services secretary Robert F. Kennedy Jr. is promoting, provides resources on the administration's new dietary guidelines, released in January, and encourages people to use Elon Musk's AI chatbot Grok to "get real answers about real food." I decided to see how Grok's advice aligns with the administration's recommendations, particularly around protein intake. The new guidelines say to get 1.2 to 1.6 grams of protein per kilogram of body weight per day--more than what was previously advised--while the new inverted food pyramid prominently features steak and other animal products.

To this end, we propose a Hierarchical Representation Learning Framework (HRLF) for the MSA task under uncertain missing modalities.

As a result, the explanation generated is painstakingly customized foreachinstance.