Generative models, such as large language models or text-to-image diffusion models, can generate relevant responses to user-given queries. Response-based vector embeddings of generative models facilitate statistical analysis and inference on a given collection of black-box generative models. The Data Kernel Perspective Space embedding is one particular method of obtaining response-based vector embeddings for a given set of generative models, already discussed in the literature. In this paper, under appropriate regularity conditions, we establish high probability concentration bounds on the sample vector embeddings for a given set of generative models, obtained through the method of Data Kernel Perspective Space embedding. Our results tell us the required number of sample responses needed in order to approximate the population-level vector embeddings with a desired level of accuracy. The algebraic tools used to establish our results can be used further for establishing concentration bounds on Classical Multidimensional Scaling embeddings in general, when the dissimilarities are observed with noise.

翻译：生成模型，如大型语言模型或文本到图像扩散模型，能够针对用户给定的查询生成相关响应。生成模型的基于响应的向量嵌入有助于对给定集合的黑盒生成模型进行统计分析与推断。数据核视角空间嵌入是一种为给定生成模型集合获取基于响应的向量嵌入的具体方法，已在文献中有所讨论。本文在适当的正则性条件下，针对通过数据核视角空间嵌入方法获得的给定生成模型集合的样本向量嵌入，建立了高概率集中界。我们的结果揭示了为以期望精度逼近总体水平向量嵌入所需的样本响应数量。用于建立我们结果的代数工具可进一步用于建立经典多维尺度嵌入在一般情况下的集中界，特别是当相异性在噪声条件下被观测时。