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:
Potential games and decentralised partially observable MDPs (Dec–POMDPs) are two commonly used models of multi–agent interaction, for static optimisation and sequential decision– making settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player’s observations of others’ actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec–POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec–POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec–POMDPs, and demonstrate our new algorithm’s performance in a box pushing problem. Our results show that we consistently outperform the state–of–the–art Dec– POMDP solver by an average of 100% across the range of noise in the observation function.
answer:
Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs


question:
We give an interpretation of the Maxi­ mum Entropy (MaxEnt) Principle in game­ theoretic terms. Based on this interpretation, we make a formal distinction between differ­ ent ways of applying Maximum Entropy dis­ tributions. MaxEnt has frequently been crit­ icized on the grounds that it leads to highly representation dependent results. Our dis­ tinction allows us to avoid this problem in many cases.
answer:

Maximum Entropy and the Glasses You are Looking Through