A0931
Title: Spectral CLTs for large language and large multimodal models
Authors: Andrej Srakar - Institute for Economic Research Ljubljana (Slovenia) [presenting]
Abstract: Since the past pioneering studies, central and noncentral limit theorems have been constantly refined and extended. Recently, another study extended this to spectral central limit theorems that are valid for additive functionals of isotropic and stationary Gaussian fields. It uses the Malliavin-Stein method and Fourier analysis techniques when $Y_t$ admits Gaussian fluctuations in a long memory context. In another recent article, existing language models are augmented with long-term memory. It proposed a framework of language models augmented with long-term memory, which enables LLMs to memorize long histories. The focus is to develop spectral central limit theorems in the context of augmented large language models, as well as to present extensions of LLM labelled, large multimodal models. The main stochastic calculus tools are derived from the Malliavin-Stein method, Fourier analysis, and free probability. Applications and extensions of the work are possible in multiple areas in probability theory, statistics, data science and econometrics, such as stochastic geometry, spherical random fields, deep neural networks and graph neural networks, causal AI and functional data analysis. Applications on datasets from finance and medical imaging are presented. In conclusion, possible Bayesian extensions are discussed.
