Concentration bounds on response-based vector embeddings of black-box generative models

2025-11-11

AI Summary

This work investigates the sampling complexity of responsive vector embeddings for black-box generative models in the Data Kernel Perspective Space (DKPS): specifically, how many model responses are required to approximate the population embedding with high probability and a prescribed accuracy. We first establish high-probability concentration bounds for response embeddings in DKPS. Then, we propose a general algebraic analytical framework that models noisy, heterogeneous distance observations as perturbed matrices, and leverage tools from random matrix theory and matrix perturbation analysis to derive a lower bound on the sample size required for embedding convergence. This theoretical guarantee enables robust statistical inference over ensembles of generative models. Experiments across multiple mainstream black-box models validate the theoretically predicted decay of embedding error with increasing sample size, confirming both the validity and practical utility of our approach.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

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.

Problem

• Establishes concentration bounds for vector embeddings of black-box generative models
• Determines required sample size for accurate population-level embedding approximation
• Extends analytical tools to noisy Classical Multidimensional Scaling embeddings

Innovation

• Concentration bounds on Data Kernel Perspective Space embeddings
• Sample size requirements for accurate population embeddings
• Algebraic tools for noisy dissimilarity multidimensional scaling