instruction:
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.
question:
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.
answer:
Improved modeling of complex systems uses hybrid neural/domain model composition, new decorrelation loss functions and extrapolative test sets 


question:
The linear transformations in converged deep networks show fast eigenvalue decay. The distribution of eigenvalues looks like a Heavy-tail distribution, where the vast majority of eigenvalues is small, but not actually zero, and only a few spikes of large eigenvalues exist.
 We use a stochastic approximator to generate histograms of eigenvalues. This allows us to investigate layers with hundreds of thousands of dimensions. We show how the distributions change over the course of image net training, converging to a similar heavy-tail spectrum across all intermediate layers.
answer:
We investigate the eigenvalues of the linear layers in deep networks and show that the distributions develop heavy-tail behavior during training.


question:
Adversarial training is by far the most successful strategy for improving robustness of neural networks to adversarial attacks. Despite its success as a defense mechanism, adversarial training fails to generalize well to unperturbed test set. We hypothesize that this poor generalization is a consequence of adversarial training with uniform perturbation radius around every training sample. Samples close to decision boundary can be morphed into a different class under a small perturbation budget, and enforcing large margins around these samples produce poor decision boundaries that generalize poorly. Motivated by this hypothesis, we propose instance adaptive adversarial training -- a technique that enforces sample-specific perturbation margins around every training sample. We show that using our approach, test accuracy on unperturbed samples improve with a marginal drop in robustness. Extensive experiments on CIFAR-10, CIFAR-100 and Imagenet datasets demonstrate the effectiveness of our proposed approach.
answer:

Instance adaptive adversarial training for improving robustness-accuracy tradeoff