Generative adversarial networks (GANs) are innovative techniques for learning generative models of complex data distributions from samples. Despite remarkable recent improvements in generating realistic images, one of their major shortcomings is the fact that in practice, they tend to produce samples with little diversity, even when trained on diverse datasets. This phenomenon, known as mode collapse, has been the main focus of several recent advances in GANs. Yet there is little understanding of why mode collapse happens and why recently proposed approaches are able to mitigate mode collapse. We propose a principled approach to handling mode collapse, which we call packing. The main idea is to modify the discriminator to make decisions based on multiple samples from the same class, either real or artificially generated. We borrow analysis tools from binary hypothesis testing-in particular the seminal result of Blackwell [6]-to prove a fundamental connection between packing and mode collapse. We show that packing naturally penalizes generators with mode collapse, thereby favoring generator distributions with less mode collapse during the training process. Numerical experiments on benchmark datasets suggests that packing provides significant improvements in practice as well.

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Introduction: This study analyzed the effectiveness of 650-nm red-light feeding instruments in the control of myopia. Methods: In this study, 164 school-aged participants diagnosed with myopia in the city of Shenzhen were enrolled in a red-light feeding instrument study. Of these, 41 were enrolled in the mild-to-moderate myopia group that received red-light feeding (RLMM group), 65 were enrolled in the mild-to-moderate myopia group that received single-vision spectacle treatment (SVSMM group), and 58 were included in the severe-myopia group that received red-light feeding (RLS group). Results: After the baseline values of the three groups were matched, the right-eye data were used for statistical analysis. The average return-visit time of each group was 60.42 days, and changes in the observation indexes before treatment and after follow-up treatment were compared. As the primary outcome, the axial length changes in the right eye of the SVSMM group (0.08 ± 0.40 mm), the RLMM group (–0.03 ± 0.11 mm), and the RLS group (−0.07 ± 0.11 mm) were compared and showed a statistical result of P < 0.001. Conclusion: The study results verified that red light had a noticeable effect on the control of myopia and that low-level red-light therapy played a vital role in the treatment of severe myopia.

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