Comparing Foundation Models using Data Kernels

By Brandon Duderstadt, Hayden S. Helm, Carey E. Priebe. arXiv.org, 2023

16 citations recorded by the source corpus.

Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for comparing foundation models involves evaluating them with aggregate metrics on various benchmark datasets. This method of model comparison is heavily dependent on the chosen evaluation metric, which makes it unsuitable for situations where the ideal metric is either not obvious or unavailable. In this work, we present a methodology for directly comparing the embedding space geometry of foundation models, which facilitates model comparison without the need for an explicit evaluation metric. Our methodology is grounded in random graph theory and enables valid hypothesis testing of embedding similarity on a per-datum basis. Further, we demonstrate how our methodology can be extended to facilitate population level model comparison. In particular, we show how our framework can induce a manifold of models equipped with a distance function that correlates strongly with several downstream metrics. We remark on the utility of this population level model comparison as a first step towards a taxonomic science of foundation models.

Subfields: Statistics and Probability, Representation & Self-Supervised Learning, Evaluation & Benchmarks

View Paper: https://arxiv.org/abs/2305.05126

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

In Representation & Self-Supervised Learning

In Evaluation & Benchmarks

Citations in the corpus

Tracking the perspectives of interacting language models (2024, methodology): “For this, we introduce an adaptation of the embedding-based data kernel presented in (Duderstadt et al., 2023).”
Jailbreak susceptibility prediction and mitigation via the behavioral geometry of models (2026, unknown): “Low-dimensional representations of language models have been constructed from internal activations [33, 22, 18, 10], model weights [2], and embeddings of model responses [16, 14, 1, 5].”
Control Charts for Multi-agent Systems (2026, unknown): “Prior work has embedded models via internal activations [8, 13], parameter weights [20], or responses to reference queries [1].”
Black-box model classification under the discriminative factorization (2026, unknown): “Low-dimensional representations of generative models can be constructed from internal activations [29, 21, 17, 10] and model weights [2, 7].”
Consistent estimation of generative model representations in the data kernel perspective space (2024, background): “Recently, empirical investigations have demonstrated the potential of embedding-based vector representations of models for capturing meaningful differences in model behavior in the context of a set of queries [10, 9, 12].”
Query-efficient model evaluation using cached responses (2026, unknown): “Some approaches construct representations by comparing internal activations across models (Duderstadt et al., 2023; Huh al., 2024; Horwitz et al., 2025) or by comparing model weights directly (Chen et al., 2025).”
Concentration bounds on response-based vector embeddings of black-box generative models (2025, unknown): “…of providing performance guarantees and unsupervised learning to investigate differences in model behaviour, various works (Faggioli et al., 2023; Duderstadt et al., 2023) explore and demonstrate the potential of response-based vector embeddings of generative models for subsequent inference…”
Investigating social alignment via mirroring in a system of interacting language models (2024, unknown): “We note that increasing the complexity of the agents will require using general black-box techniques (Duderstadt et al., 2024; Helm et al., 2024b; Acharyya et al., 2024; Helm et al., 2024a) to study agent, group, and system dynamics.”
A Model of the Language Process (2026, unknown): “We call this curve the "temporal control curve," and conjecture that the model vectors constituting this curve can be applied to tasks including model comparison (Duderstadt et al., 2024), model level inference (Helm et al., 2025), and model perspective tracking (Helm et al., 2024).”
Fusing Multi‐ and Hyperspectral Satellite Data for Harmful Algal Bloom Monitoring With Self‐Supervised and Hierarchical Deep Learning (2025, unknown): “Minimal variance and a small sample size do not allow for further insight at this time.”
The View From Space: Navigating Instrumentation Differences with EOFMs (2025, unknown): “This is based on the intuitive notion that similarity between data points is a perspective on the overall configuration of the space Duderstadt u. a. (2023); Tavares u. a. (2024) .”
Development and Application of Self-Supervised Machine Learning for Smoke Plume and Active Fire Identification from the FIREX-AQ Datasets (2025, unknown): “More robust ways to evaluate representative capabilities are emerging in around large language models (LLMs), and much of this can be ported to computer vision, and specifically deep learning for Earth Observations [69].”
A Statistical Turing Test for Generative Models (2023, background): “Recent efforts such as the living benchmarks of holistic evaluation [24] for natural language processing tasks and the use of data kernels to understand differences in the embedding spaces of models [10] are important strides for understanding absolute and relative model capabilities, respectively.”
Extracting information from fine-tuned weights (unknown): “In the same setting, [4] proposes representing models as an input-dependent nearest neighbor graph and shows that the geometry of the representations encodes meaningful information about each model’s training data.”