In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Q: To provide principled ways of designing proper Deep Neural Network (DNN) models, it is essential to understand the loss surface of DNNs under realistic assumptions. We introduce interesting aspects for understanding the local minima and overall structure of the loss surface. The parameter domain of the loss surface can be decomposed into regions in which activation values (zero or one for rectified linear units) are consistent. We found that, in each region, the loss surface have properties similar to that of linear neural networks where every local minimum is a global minimum. This means that every differentiable local minimum is the global minimum of the corresponding region. We prove that for a neural network with one hidden layer using rectified linear units under realistic assumptions. There are poor regions that lead to poor local minima, and we explain why such regions exist even in the overparameterized DNNs.

A: The loss surface of neural networks is a disjoint union of regions where every local minimum is a global minimum of the corresponding region.
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Q: Deterministic models are approximations of reality that are often easier to build and interpret than stochastic alternatives.
Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic models in practice.
Observation and process noise need to be added to adapt deterministic models to behave stochastically, such that they are capable of explaining and extrapolating from noisy data.
Adding process noise to deterministic simulators can induce a failure in the simulator resulting in no return value for certain inputs -- a property we describe as ''brittle.''
We investigate and address the wasted computation that arises from these failures, and the effect of such failures on downstream inference tasks.
We show that performing inference in this space can be viewed as rejection sampling, and train a conditional normalizing flow as a proposal over noise values such that there is a low probability that the simulator crashes, increasing computational efficiency and inference fidelity for a fixed sample budget when used as the proposal in an approximate inference algorithm.

A: We learn a conditional autoregressive flow to propose perturbations that don't induce simulator failure, improving inference performance.
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Q: Learning high-quality word embeddings is of significant importance in achieving better performance in many down-stream learning tasks. On one hand, traditional word embeddings are trained on a large scale corpus for general-purpose tasks, which are often sub-optimal for many domain-specific tasks. On the other hand, many domain-specific tasks do not have a large enough domain corpus to obtain high-quality embeddings. We observe that domains are not isolated and a small domain corpus can leverage the learned knowledge from many past domains to augment that corpus in order to generate high-quality embeddings. In this paper, we formulate the learning of word embeddings as a lifelong learning process. Given knowledge learned from many previous domains and a small new domain corpus, the proposed method can effectively generate new domain embeddings by leveraging a simple but effective algorithm and a meta-learner, where the meta-learner is able to provide word context similarity information at the domain-level. Experimental results demonstrate that the proposed method can effectively learn new domain embeddings from a small corpus and past domain knowledges
ootnote{We will release the code after final revisions.}. We also demonstrate that general-purpose embeddings trained from a large scale corpus are sub-optimal in domain-specific tasks.

A:
learning better domain embeddings via lifelong learning and meta-learning
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