The representation of complex phenomena via combinations of simple discrete features is a hallmark of human cognition. But it is not clear exactly how (or whether) discrete features can effectively represent the complex probabilistic fabric of the environment. This article introduces information-theoretic tools for quantifying the fidelity and efficiency of a featural representation with respect to a probability model. In this framework, a feature or combination of features is "faithful" to the extent that knowing the value of the features reduces uncertainty about the true state of the world. In a single dimension, a discrete feature is faithful if the values of the feature correspond isomorphically to distinct classes in the probability model. But in multiple dimensions, the situation is more complicated: The fidelity of each feature depends on the direction in multidimensional feature space in which the feature is projected from the underlying distribution. More interestingly, distributions may be more effectively represented by combinations of projected features-that is, compositionality. For any given distribution, a variety of compositional forms (features and combination rules) are possible, which can be quite different from one another, entailing different degrees of fidelity, different numbers of features, and even different induced regularities. This article proposes three specific criteria for a compositional representation: fidelity, simplicity, and robustness. The information-theoretic framework introduces a new and potentially useful way to look at the problem of compositionality in human mental representation. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

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组合心理表征的概率起源。

通过简单离散特征的组合来表示复杂现象是人类认知的标志。但目前尚不清楚离散特征如何（或是否）能够有效地表示环境的复杂概率结构。本文介绍了用于量化概率模型特征表示的保真度和效率的信息论工具。在这个框架中，一个特征或特征组合是“忠实的”，因为知道这些特征的值可以减少关于世界真实状态的不确定性。在单一维度中，如果特征值同构对应于概率模型中的不同类，则离散特征是忠实的。但在多维中，情况更加复杂：每个特征的保真度取决于多维特征空间中特征从底层分布投影的方向。更有趣的是，分布可以通过投影特征的组合（即组合性）更有效地表示。对于任何给定的分布，可能有多种组合形式（特征和组合规则），这些组合形式可能彼此截然不同，需要不同程度的保真度、不同数量的特征，甚至不同的归纳规律。本文提出了组合表示的三个具体标准：保真度、简单性和鲁棒性。信息论框架引入了一种新的且可能有用的方法来看待人类心理表征中的组合性问题。（PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。