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.

Ex Input:
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%.

Ex Output:
We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation.

Ex Input:
While counter machines have received little attention in theoretical computer science since the 1960s, they have recently achieved a newfound relevance to the field of natural language processing (NLP). Recent work has suggested that some strong-performing recurrent neural networks utilize their memory as counters. Thus, one potential way to understand the sucess of these networks is to revisit the theory of counter computation. Therefore, we choose to study the abilities of real-time counter machines as formal grammars. We first show that several variants of the counter machine converge to express the same class of formal languages. We also prove that counter languages are closed under complement, union, intersection, and many other common set operations. Next, we show that counter machines cannot evaluate boolean expressions, even though they can weakly validate their syntax. This has implications for the interpretability and evaluation of neural network systems: successfully matching syntactic patterns does not guarantee that a counter-like model accurately represents underlying semantic structures. Finally, we consider the question of whether counter languages are semilinear. This work makes general contributions to the theory of formal languages that are of particular interest for the interpretability of recurrent neural networks.

Ex Output:
We study the class of formal languages acceptable by real-time counter automata, a model of computation related to some types of recurrent neural networks.

Ex Input:
Given the fast development of analysis techniques for NLP and speech
processing systems, few systematic studies have been conducted to
compare the strengths and weaknesses of each method. As a step in
this direction we study the case of representations of phonology in
neural network models of spoken language. We use two commonly applied
analytical techniques, diagnostic classifiers and representational
similarity analysis, to quantify to what extent neural activation
patterns encode phonemes and phoneme sequences. We manipulate two
factors that can affect the outcome of analysis. First, we investigate
the role of learning by comparing neural activations extracted from
trained versus randomly-initialized models. Second, we examine the
temporal scope of the activations by probing both local activations
corresponding to a few milliseconds of the speech signal, and global
activations pooled over the whole utterance. We conclude that
reporting analysis results with randomly initialized models is
crucial, and that global-scope methods tend to yield more consistent
and interpretable results and we recommend their use as a complement
to local-scope diagnostic methods.

Ex Output:
We study representations of phonology in neural network models of spoken language with several variants of analytical techniques.