Sobolev GAN google
“Sobolev Integral Probability Metric”

Evolutionary Generative Adversarial Network (E-GAN) google
Generative adversarial networks (GAN) have been effective for learning generative models for real-world data. However, existing GANs (GAN and its variants) tend to suffer from training problems such as instability and mode collapse. In this paper, we propose a novel GAN framework called evolutionary generative adversarial networks (E-GAN) for stable GAN training and improved generative performance. Unlike existing GANs, which employ a pre-defined adversarial objective function alternately training a generator and a discriminator, we utilize different adversarial training objectives as mutation operations and evolve a population of generators to adapt to the environment (i.e., the discriminator). We also utilize an evaluation mechanism to measure the quality and diversity of generated samples, such that only well-performing generator(s) are preserved and used for further training. In this way, E-GAN overcomes the limitations of an individual adversarial training objective and always preserves the best offspring, contributing to progress in and the success of GANs. Experiments on several datasets demonstrate that E-GAN achieves convincing generative performance and reduces the training problems inherent in existing GANs. …

Substochastic Monte Carlo (SSMC) google
In this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization algorithms in their own right. In SSMC, a population of walkers is initialized according to a known distribution on an arbitrary search space and varied into the solution of some optimization problem of interest. The first argument of this paper shows how an existing classical algorithm, ‘Go-With-The-Winners’ (GWW), is a limiting case of SSMC when restricted to binary search and particular driving dynamics. Although limiting to GWW, SSMC is more general. We show that (1) GWW can be efficiently simulated within the SSMC framework, (2) SSMC can be exponentially faster than GWW, (3) by naturally incorporating structural information, SSMC can exponentially outperform the quantum algorithm that first inspired it, and (4) SSMC exhibits desirable search features in general spaces. Our approach combines ideas from genetic algorithms (GWW), theoretical probability (Fleming-Viot processes), and quantum computing. Not only do we demonstrate that SSMC is often more efficient than competing algorithms, but we also hope that our results connecting these disciplines will impact each independently. An implemented version of SSMC has previously enjoyed some success as a competitive optimization algorithm for Max-$k$-SAT. …

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