Softmax mixture ensembles for leveraging LLM output

This project introduces and examines softmax mixture ensemble models to address contemporary questions related to the evaluation and interpretation of data generated by trained large language models (LLMs). These statistical models will help summarize varied document corpora by identifying their semantically meaningful latent topics. Current LLMs contain billions of parameters, which makes them difficult to interpret and use directly in subsequent analyses. There is an urgent need for corpus summaries that strike a balance between the complexity of the generating models and a user-friendly representation. This project aims to develop new metrics based on the interpretable corpus summaries to provide critical insights into the similarities and differences between human-generated and AI-generated text. This research develops computationally efficient inferential methods, with sharp mathematical guarantees, for learning and analyzing softmax mixture parameters from data consisting of a collection of samples, each modeled as mixtures with common mixture components and sample-specific coefficients. The softmax mixture ensemble model will be shown to be a crucial building block in a more complex mixture-of-experts model. The project will provide experimental evidence for the benefits of this framework in analyzing LLM data. Solving the statistical questions of this project requires bringing to bear tools from optimization theory, probability and high-dimensional statistics, while addressing the application questions will require tools from computer science, specifically from the areas of natural language processing (NLP) and, more generally, AI. The ultimate goal is to develop procedures which yield accurate, robust, and interpretable results, readily applicable to scientific applications. The central goals of this research are parameter identifiability in softmax ensemble models, polynomial-time algorithms for parameter estimation in high-dimensional softmax ensemble models with dense and sparse parametrization, finite sample (minimax) guarantees, asymptotic inference for parameter estimates in softmax ensemble models, as well as the development of necessary tools for evaluating LLM output in open-ended text generation. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.