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]: 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.
[A]: 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.


[Q]: Voice Conversion (VC) is a task of converting perceived speaker identity from a source speaker to a particular target speaker. Earlier approaches in the literature primarily find a mapping between the given source-target speaker-pairs. Developing mapping techniques for many-to-many VC using non-parallel data, including zero-shot learning remains less explored areas in VC. Most of the many-to-many VC architectures require training data from all the target speakers for whom we want to convert the voices. In this paper, we propose a novel style transfer architecture, which can also be extended to generate voices even for target speakers whose data were not used in the training (i.e., case of zero-shot learning). In particular, propose Adaptive Generative Adversarial Network (AdaGAN), new architectural training procedure help in learning normalized speaker-independent latent representation, which will be used to generate speech with different speaking styles in the context of VC. We compare our results with the state-of-the-art StarGAN-VC architecture. In particular, the AdaGAN achieves 31.73%, and 10.37% relative improvement compared to the StarGAN in MOS tests for speech quality and speaker similarity, respectively. The key strength of the proposed architectures is that it yields these results with less computational complexity. AdaGAN is 88.6% less complex than StarGAN-VC in terms of FLoating Operation Per Second (FLOPS), and 85.46% less complex in terms of trainable parameters.  
[A]: Novel adaptive instance normalization based GAN framework for non parallel many-to-many and zero-shot VC. 


[Q]: We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any definition of the semantic information, the problem might seem ill-posed. Specifically, in typical cases, it seems possible to build infinitely many alternative mappings  from every target mapping. This apparent ambiguity stands in sharp contrast to the recent empirical success in solving this problem.

 We identify the abstract notion of aligning two domains in a semantic way with concrete terms of minimal relative complexity. A theoretical framework for measuring the complexity of compositions of functions is developed in order to show that it is reasonable to expect the minimal complexity mapping to be unique. The measured complexity used is directly related to the depth of the neural networks being learned and a semantically aligned mapping could then be captured simply by learning using architectures that are not much bigger than the minimal architecture.

 Various predictions are made based on the hypothesis that semantic alignment can be captured by the minimal mapping. These are verified extensively. In addition, a new mapping algorithm is proposed and shown to lead to better mapping results.
[A]:
Our hypothesis is that given two domains, the lowest complexity mapping that has a low discrepancy approximates the target mapping.