instruction:
In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
question:
The preimage of the activities of all the nodes at a certain level of a deep network is the set of inputs that result in the same node activity. For fully connected multi layer rectifier networks we demonstrate how to compute the preimages of activities at arbitrary levels from knowledge of the parameters in a deep rectifying network by disregarding the effects of max-pooling. If the preimage set of a certain activity in the network contains elements from more than one class it means that these classes are irreversibly mixed. This implies that preimage sets which are piecewise linear manifolds are building blocks for describing the input manifolds specific classes, i.e. all preimages should ideally be from the same class. We believe that the knowledge of how to compute preimages will be valuable in understanding the efficiency displayed by deep learning networks and could potentially be used in designing more efficient training algorithms
answer:
THE PREIMAGE OF RECTIFIER NETWORK ACTIVITIES

question:
This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable convex functions.
answer:
Agglomerative Bregman Clustering

question:
We introduce a method for transliteration generation that can produce transliterations in every language. Where previous results are only as multilingual as Wikipedia, we show how to use training data from Wikipedia as surrogate training for any language. Thus, the problem becomes one of ranking Wikipedia languages in order of suitability with respect to a target language. We introduce several task-specific methods for ranking languages, and show that our approach is comparable to the oracle ceiling, and even outperforms it in some cases.
answer:
Transliteration in Any Language with Surrogate Languages