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

arXiv: https://arxiv.org/abs/2511.08307 · HTML: https://mlsanity.com/paper/2511.08307/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 13 of 13)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [VQGAN-CLIP: Open Domain Image Generation and Editing with Natural Language Guidance](https://mlsanity.com/paper/2204.08583/) (2022)
- [Planning with Large Language Models for Code Generation](https://mlsanity.com/paper/2303.05510/) (2023)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Perspectives on Large Language Models for Relevance Judgment](https://mlsanity.com/paper/2304.09161/) (2023)
- [Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics](https://mlsanity.com/paper/1605.00353/) (2016)
- [Evaluating the Performance of Large Language Models via Debates](https://mlsanity.com/paper/2406.11044/) (2024)
- [Comparing Foundation Models using Data Kernels](https://mlsanity.com/paper/2305.05126/) (2023)
- [Tracking the perspectives of interacting language models](https://mlsanity.com/paper/2406.11938/) (2024)
- [Consistent estimation of generative model representations in the data kernel perspective space](https://mlsanity.com/paper/2409.17308/) (2024)
- [Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels](https://mlsanity.com/paper/2212.05053/) (2022)

## Built on by (most cited first, 1 of 1)

- [Query-efficient model evaluation using cached responses](https://mlsanity.com/paper/2605.07096/) (2026)

## Abstract (arXiv)

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.