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arXiv 2307.01422cs.LG
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生成流网络:马尔可夫链视角

Generative Flow Networks: a Markov Chain Perspective

Université de Montréal(蒙特利尔大学);Mila – Quebec AI Institute(米拉-魁北克人工智能研究所)

Tristan Deleu, Yoshua Bengio

AI总结:

本文从马尔可夫链视角形式化生成流网络(GFlowNets),将其统一视为循环马尔可夫链,并与MCMC方法进行理论对比,揭示两者异同。

摘要:

虽然马尔可夫链蒙特卡洛方法(MCMC)为从定义到归一化的概率分布中采样提供了一个通用框架,但当目标分布高度多模态时,它们往往收敛缓慢。最近,生成流网络(GFlowNets)被提出作为一种替代框架,通过将采样视为序贯决策问题,在样本具有清晰组合结构时缓解这一问题。尽管它们最初是从流网络的角度引入的,但GFlowNets的最新进展越来越多地从马尔可夫链文献中汲取灵感,完全绕过了对流的需求。在本文中,我们形式化了这种联系,并利用马尔可夫链为GFlowNets提供了一个新视角,表明无论状态空间的性质如何,GFlowNets都可以统一视为循环马尔可夫链。将GFlowNets置于与MCMC方法相同的理论框架下,也使我们能够识别两种框架之间的相似性,最重要的是突出它们的差异。

英文摘要:

While Markov chain Monte Carlo methods (MCMC) provide a general framework to sample from a probability distribution defined up to normalization, they often suffer from slow convergence to the target distribution when the latter is highly multi-modal. Recently, Generative Flow Networks (GFlowNets) have been proposed as an alternative framework to mitigate this issue when samples have a clear compositional structure, by treating sampling as a sequential decision making problem. Although they were initially introduced from the perspective of flow networks, the recent advances of GFlowNets draw more and more inspiration from the Markov chain literature, bypassing completely the need for flows. In this paper, we formalize this connection and offer a new perspective for GFlowNets using Markov chains, showing a unifying view for GFlowNets regardless of the nature of the state space as recurrent Markov chains. Positioning GFlowNets under the same theoretical framework as MCMC methods also allows us to identify the similarities between both frameworks, and most importantly to highlight their

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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