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.

Example Input: We present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. Experimentally we show OT-GAN to be highly stable when trained with large mini-batches, and we present state-of-the-art results on several popular benchmark problems for image generation.
Example Output: An extension of GANs combining optimal transport in primal form with an energy distance defined in an adversarially learned feature space.

Example 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.
Example 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.

Example Input: Offset regression is a standard method for spatial localization in many vision tasks, including human pose estimation, object detection, and instance segmentation. However,
if high localization accuracy is crucial for a task, convolutional neural networks will offset regression
usually struggle to deliver. This can be attributed to the locality of the convolution operation, exacerbated by variance in scale, clutter, and viewpoint. An even more fundamental issue is the multi-modality of real-world images. As a consequence, they cannot be approximated adequately using a single mode model. Instead, we propose to use mixture density networks (MDN) for offset regression, allowing the model to manage various modes efficiently and learning to predict full conditional density of the outputs given the input. On 2D human pose estimation in the wild, which requires accurate localisation of body keypoints, we show that this yields significant improvement in localization accuracy. In particular, our experiments reveal viewpoint variation as the dominant multi-modal factor. Further, by carefully initializing MDN parameters, we do not face any instabilities in training, which is known to be a big obstacle for widespread deployment of MDN. The method can be readily applied to any task with a spatial regression component. Our findings highlight the multi-modal nature of real-world vision, and the significance of explicitly accounting for viewpoint variation, at least when spatial localization is concerned.

Example Output:
We use mixture density networks to do full conditional density estimation for spatial offset regression and apply it to the human pose estimation task.