扩散模型与概念形成
Diffusion Models and Concept Formation
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中文总结 AI 辅助
本文论证扩散模型隐式执行与Cobweb相同的概念层次构建，在噪声边际众数中形成对应原型树，并在中间噪声水平涌现基本层级，为扩散模型提供认知解释并赋予Cobweb连续可扩展实现。
中文摘要 AI 辅助
人类将知识组织成一个概念分类体系，该体系具有嵌套的抽象层级，并包含一个“基本层级”，在此层级上，人们以最小的认知努力识别和命名对象。Cobweb是这种能力的经典认知模型，它是一个增量学习器，通过最大化类别效用来构建概率概念层次结构。我们认为，扩散模型虽然是为图像合成而设计的，但隐式地执行了相同的计算。扩散模型的噪声边际分布是数据分布的高斯平滑，这些边际分布的众数形成一个层次结构，该层次结构在四个方面对应于Cobweb树的概率原型。两者都是层次密度模型，都是具有高斯原型的层次贝叶斯模型，都将分类视为降低不确定性的分数跟踪，并且在两者中都会出现一个基本层级。我们将扩散模型的基本层级定位于一个中间噪声水平，在该水平上，最近的分析表明反向过程会确定样本的类别身份。这两种模型的主要区别在于它们表示和学习分类体系的方式。Cobweb增量地学习一棵离散树，而扩散模型则将连续的、可插值的层次结构编码在单个学习到的、拟合数据分布的分数场中。我们在MNIST和Fashion-MNIST上通过模式查找恢复扩散层次结构，并比较两种模型的基本层级，从而检验了这种对应关系。这将扩散模型重新定义为概念形成的认知模型，并为Cobweb提供了一种连续的、可扩展的实现。
英文摘要
Humans organize knowledge into a taxonomy of concepts with nested levels of abstraction and a \emph{basic level} at which people recognize and name objects with the least cognitive effort. Cobweb is a classic cognitive account of this ability, an incremental learner that builds a probabilistic concept hierarchy by maximizing category utility. We argue that diffusion models, although designed for image synthesis, implicitly perform the same computation. The noisy marginals of a diffusion model are Gaussian smoothings of the data distribution, and the modes of these marginals form a hierarchy that corresponds to a Cobweb tree of probabilistic prototypes in four respects. Both are hierarchical density models, both are hierarchical-Bayesian models with Gaussian prototypes, both treat categorization as score-following that reduces uncertainty, and in both a basic level emerges. We locate this basic level for a diffusion model at an intermediate noise level, where recent analyses show that the reverse process commits to the class identity of a sample. The two models differ mainly in how they represent and learn the taxonomy. Cobweb learns a discrete tree incrementally, whereas a diffusion model encodes a continuous, interpolable hierarchy in a single learned score field fit to the data distribution. We test the correspondence on MNIST and Fashion-MNIST by recovering the diffusion hierarchy through mode-finding and comparing the basic levels of the two models. This reframes diffusion as a cognitive model of concept formation and offers Cobweb a continuous, scalable instantiation.
发表机构
- Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。
