Efficiently sampling from un-normalized target distributions is a fundamental problem in scientific computing and machine learning. Traditional approaches such as Markov Chain Monte Carlo (MCMC) guarantee asymptotically unbiased samples from such distributions but suffer from computational inefficiency, particularly when dealing with high-dimensional targets, as they require numerous iterations to generate a batch of samples. In this paper, we introduce an efficient and scalable neural implicit sampler that overcomes these limitations. The implicit sampler can generate large batches of samples with low computational costs by leveraging a neural transformation that directly maps easily sampled latent vectors to target samples without the need for iterative procedures. To train the neural implicit samplers, we introduce two novel methods: the KL training method and the Fisher training method. The former method minimizes the Kullback-Leibler divergence, while the latter minimizes the Fisher divergence between the sampler and the target distributions. By employing the two training methods, we effectively optimize the neural implicit samplers to learn and generate from the desired target distribution. To demonstrate the effectiveness, efficiency, and scalability of our proposed samplers, we evaluate them on three sampling benchmarks with different scales.

翻译：从未归一化的目标分布中高效采样是科学计算和机器学习中的一个基本问题。传统方法如马尔可夫链蒙特卡罗（MCMC）能保证从此类分布中获得渐近无偏的样本，但存在计算效率低下的问题，尤其是在处理高维目标分布时，它们需要大量迭代才能生成一批样本。本文提出一种高效且可扩展的神经隐式采样器以克服这些限制。该隐式采样器通过利用神经变换，将易于采样的隐向量直接映射为目标样本，无需迭代过程，从而能够以较低计算成本生成大批量样本。为训练神经隐式采样器，我们引入两种新方法：KL训练方法与Fisher训练方法。前者最小化采样器与目标分布间的Kullback-Leibler散度，后者最小化二者间的Fisher散度。通过采用这两种训练方法，我们有效优化了神经隐式采样器，使其能够学习并生成所需的目标分布。为验证所提出采样器的有效性、效率与可扩展性，我们在三种不同规模的采样基准测试上对其进行了评估。