This gives rise to a rich collection oftopological relationships and conditions under which VE models are optimal for planning. Despite this effort, relatively little is known about the planning performance of models that fail to satisfy these conditions.

From Figure 1(a), learning multiple linear sub-models and averaging the predictions (ensemble) is still a linear model, so it cannot tackleXOR problem. We compare the training cost of all methods from the two aspects;1). Thesub-model training enables themost adversarial attacks ofsub-models could be successfully defended. In particular, we train two kinds of models to defend against the attacks: 1). FromFigure2(a)and2(b),when0.01 ϵ 0.04, SoE without the collaboration training achieves a similar robustness compared with SoE.

Inmany cases, increasing model capacity beyond the memory limit of a single acceleratorhas required developing special algorithms orinfrastructure. These solutions are often architecture-specific and do not transfer to other tasks.

While capable of generating photo-realistic images, these models often produce unrealistic samples which fall outside of the data manifold.

The ability to encode informative functional beliefs in BNN priors can significantly reduce the bias and uncertainty of the posterior predictive, especially in regions of input space sparsely coveredbytraining data[27].

The Transformer model has achieved state-of-the-art performance in many sequence modeling tasks. However,howtoleverage model capacity with largeor variable depths is still an open challenge.

Backdoor attack, which poisons asmall number of training samples by inserting backdoor triggers, is a typical threat to security.

The Transformer model has achieved state-of-the-art performance in many sequence modeling tasks. However, how to leverage model capacity with large or variable depths is still an open challenge. We present a probabilistic framework to automatically learn which layer(s) to use by learning the posterior distributions of layer selection. As an extension of this framework, we propose a novel method to train one shared Transformer network for multilingual machine translation with different layer selection posteriors for each language pair. The proposed method alleviates the vanishing gradient issue and enables stable training of deep Transformers (e.g. 100 layers). We evaluate on WMT English-German machine translation and masked language modeling tasks, where our method outperforms existing approaches for training deeper Transformers. Experiments on multilingual machine translation demonstrate that this approach can effectively leverage increased model capacity and bring universal improvement for both many-to-one and one-to-many translation with diverse language pairs.