标题： 知识作为遍历性的打破 显示英文标题

标题： Knowledge as a Breaking of Ergodicity

摘要： 我们构建了一个热力学势，可以指导定义在一组二值自由度上的生成模型的训练。 我们主张，在描述简化以使生成模型在计算上易于管理时，该势会发展出多个极小值。 这与生成模型本身的自由能真正出现多个极小值相呼应。 通常情况下，使用 N 个二值自由度的训练样本数量远低于完整相空间大小 2^N。 我们认为，未表示的构型应被视为由一个高温相组成，与构成训练集的构型之间存在广泛的能量间隙。 因此，训练相当于对自由能曲面进行采样，该曲面以一组不同的束缚态库的形式呈现，每个束缚态都破坏了遍历性。 这种遍历性破坏防止逃逸到包含高温相的状态的近连续区域；因此，它是正常功能所必需的。 然而，它可能会有局限训练集中表示不足的模式访问的副作用。 同时，库内的遍历性破坏使学习和检索变得复杂。 作为一种补救措施，可以同时采用多个生成模型——每个自由能极小值对应一个模型。 显示英文摘要

摘要： We construct a thermodynamic potential that can guide training of a generative model defined on a set of binary degrees of freedom. We argue that upon reduction in description, so as to make the generative model computationally-manageable, the potential develops multiple minima. This is mirrored by the emergence of multiple minima in the free energy proper of the generative model itself. The variety of training samples that employ N binary degrees of freedom is ordinarily much lower than the size 2^N of the full phase space. The non-represented configurations, we argue, should be thought of as comprising a high-temperature phase separated by an extensive energy gap from the configurations composing the training set. Thus, training amounts to sampling a free energy surface in the form of a library of distinct bound states, each of which breaks ergodicity. The ergodicity breaking prevents escape into the near continuum of states comprising the high-temperature phase; thus it is necessary for proper functionality. It may however have the side effect of limiting access to patterns that were underrepresented in the training set. At the same time, the ergodicity breaking within the library complicates both learning and retrieval. As a remedy, one may concurrently employ multiple generative models -- up to one model per free energy minimum.