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.

Q: 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%.

A: We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. 
****
Q: Neural networks can converge faster with help from a smarter batch selection strategy. In this regard, we propose Ada-Boundary, a novel adaptive-batch selection algorithm that constructs an effective mini-batch according to the learning progress of the model.Our key idea is to present confusing samples what the true label is. Thus, the samples near the current decision boundary are considered as the most effective to expedite convergence. Taking advantage of our design, Ada-Boundary maintains its dominance in various degrees of training difficulty. We demonstrate the advantage of Ada-Boundary by extensive experiments using two convolutional neural networks for three benchmark data sets. The experiment results show that Ada-Boundary improves the training time by up to 31.7% compared with the state-of-the-art strategy and by up to 33.5% compared with the baseline strategy.

A: We suggest a smart batch selection technique called Ada-Boundary.
****
Q: This paper gives a rigorous analysis of trained Generalized Hamming Networks (GHN) proposed by Fan (2017) and discloses an interesting finding about GHNs, i.e. stacked convolution layers in a GHN is equivalent to a single yet wide convolution layer. The revealed equivalence, on the theoretical side, can be regarded as a constructive manifestation of the universal approximation theorem Cybenko (1989); Hornik (1991). In practice, it has profound and multi-fold implications. For network visualization, the constructed deep epitomes at each layer provide a visualization of network internal representation that does not rely on the input data. Moreover, deep epitomes allows the direct extraction of features in just one step, without resorting to regularized optimizations used in existing visualization tools.

A:
bridge the gap in soft computing
****