Data Kernel Perspective Space Performance Guarantees for Synthetic Data from Transformer Models

TL;DR

This paper introduces Data Kernel Perspective Space (DKPS), a mathematical framework that provides performance guarantees for synthetic data generated by transformer models, addressing the unpredictability of their outputs.

Contribution

The paper develops DKPS, a novel theoretical approach that offers statistical guarantees on the quality of transformer-generated synthetic data for downstream tasks.

Findings

DKPS provides concrete performance guarantees for synthetic data.

DKPS elucidates downstream task performance, such as translation and preference optimization.

Mathematical derivation of DKPS supports its application in real-world models.

Abstract

Scarcity of labeled training data remains the long pole in the tent for building performant language technology and generative AI models. Transformer models -- particularly LLMs -- are increasingly being used to mitigate the data scarcity problem via synthetic data generation. However, because the models are black boxes, the properties of the synthetic data are difficult to predict. In practice it is common for language technology engineers to 'fiddle' with the LLM temperature setting and hope that what comes out the other end improves the downstream model. Faced with this uncertainty, here we propose Data Kernel Perspective Space (DKPS) to provide the foundation for mathematical analysis yielding concrete statistical guarantees for the quality of the outputs of transformer models. We first show the mathematical derivation of DKPS and how it provides performance guarantees. Next we show how DKPS performance guarantees can elucidate performance of a downstream task, such as neural machine translation models or LLMs trained using Contrastive Preference Optimization (CPO). Limitations of the current work and future research are also discussed.