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: Combining domain knowledge models with neural models has been challenging. End-to-end trained neural models often perform better (lower Mean Square Error) than domain knowledge models or domain/neural combinations, and the combination is inefficient to train. In this paper, we demonstrate that by composing domain models with machine learning models, by using extrapolative testing sets, and invoking decorrelation objective functions, we create models which can predict more complex systems. The models are interpretable, extrapolative, data-efficient, and capture predictable but complex non-stochastic behavior such as unmodeled degrees of freedom and systemic measurement noise. We apply this improved modeling paradigm to several simulated systems and an actual physical system in the context of system identification. Several ways of composing domain models with neural models are examined for time series, boosting, bagging, and auto-encoding on various systems of varying complexity and non-linearity. Although this work is preliminary, we show that the ability to combine models is a very promising direction for neural modeling.

A: Improved modeling of complex systems uses hybrid neural/domain model composition, new decorrelation loss functions and extrapolative test sets
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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: This work presents a method for active anomaly detection which can be built upon existing deep learning solutions for unsupervised anomaly detection. We show that a prior needs to be assumed on what the anomalies are, in order to have performance guarantees in unsupervised anomaly detection. We argue that active anomaly detection has, in practice, the same cost of unsupervised anomaly detection but with the possibility of much better results. To solve this problem, we present a new layer that can be attached to any deep learning model designed for unsupervised anomaly detection to transform it into an active method, presenting results on both synthetic and real anomaly detection datasets.

A:
A method for active anomaly detection. We present a new layer that can be attached to any deep learning model designed for unsupervised anomaly detection to transform it into an active method.
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