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:
We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation.   This characterization also leads to an algorithm for projecting a convolutional layer onto an operator-norm ball. We show that this is an effective regularizer;  for example, it improves the test error of a deep residual network using batch normalization on CIFAR-10 from 6.2% to 5.3%.
answer:
We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. 


question:
Imitation learning aims to inversely learn a policy from expert demonstrations, which has been extensively studied in the literature for both single-agent setting with Markov decision process (MDP) model, and multi-agent setting with Markov game (MG) model. However, existing approaches for general multi-agent Markov games are not applicable to multi-agent extensive Markov games, where agents make asynchronous decisions following a certain order, rather than simultaneous decisions. We propose a novel framework for asynchronous multi-agent generative adversarial imitation learning (AMAGAIL) under general extensive Markov game settings, and the learned expert policies are proven to guarantee subgame perfect equilibrium (SPE), a more general and stronger equilibrium than Nash equilibrium (NE). The experiment results demonstrate that compared to state-of-the-art baselines, our AMAGAIL model can better infer the policy of each expert agent using their demonstration data collected from asynchronous decision-making scenarios (i.e., extensive Markov games).
answer:
This paper extends the multi-agent generative adversarial imitation learning to extensive-form Markov games.


question:
Recent years have witnessed two seemingly opposite developments of deep convolutional neural networks (CNNs). On one hand, increasing the density of CNNs by adding cross-layer connections achieve higher accuracy. On the other hand, creating sparsity structures through regularization and pruning methods enjoys lower computational costs. In this paper, we bridge these two by proposing a new network structure with locally dense yet externally sparse connections. This new structure uses dense modules, as basic building blocks and then sparsely connects these modules via a novel algorithm during the training process. Experimental results demonstrate that the locally dense yet externally sparse structure could acquire competitive performance on benchmark tasks (CIFAR10, CIFAR100, and ImageNet) while keeping the network structure slim.
answer:

In this paper, we explore an internal dense yet external sparse network structure of deep neural networks and analyze its key properties.