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.
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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: In this work we consider the stochastic minimization of nonsmooth convex loss functions, a central problem in machine learning. We propose a novel algorithm called Accelerated Nonsmooth Stochastic Gradient Descent (ANSGD), which exploits the structure of common nonsmooth loss functions to achieve optimal convergence rates for a class of problems including SVMs. It is the first stochastic algorithm that can achieve the optimal O(1/t) rate for minimizing nonsmooth loss functions (with strong convexity). The fast rates are confirmed by empirical comparisons, in which ANSGD significantly outperforms previous subgradient descent algorithms including SGD.

Answer: Stochastic Smoothing for Nonsmooth Minimizations: Accelerating SGD by Exploiting Structure

Question: Biological neural networks are systems of extraordinary computational capabilities shaped by evolution, development, and lifetime learning. The interplay of these elements leads to the emergence of adaptive behavior and intelligence, but the complexity of the whole system of interactions is an obstacle to the understanding of the key factors at play. Inspired by such intricate natural phenomena, Evolved Plastic Artificial Neural Networks (EPANNs) use simulated evolution in-silico to breed plastic neural networks, artificial systems composed of sensors, outputs, and plastic components that change in response to sensory-output experiences in an environment. These systems may reveal key algorithmic ingredients of adaptation, autonomously discover novel adaptive algorithms, and lead to hypotheses on the emergence of biological adaptation. EPANNs have seen considerable progress over the last two decades. Current scientific and technological advances in artificial neural networks are now setting the conditions for radically new approaches and results. In particular, the limitations of hand-designed structures and algorithms currently used in most deep neural networks could be overcome by more flexible and innovative solutions. This paper brings together a variety of inspiring ideas that define the field of EPANNs. The main computational methods and results are reviewed. Finally, new opportunities and developments are presented.

Answer:
Born to Learn: the Inspiration, Progress, and Future of Evolved Plastic Artificial Neural Networks