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Computer Science > Machine Learning

arXiv:2402.03175 (cs)
[Submitted on 5 Feb 2024]

Title:The Matrix: A Bayesian learning model for LLMs

Authors:Siddhartha Dalal, Vishal Misra
View a PDF of the paper titled The Matrix: A Bayesian learning model
for LLMs, by Siddhartha Dalal and Vishal Misra
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    Abstract:In this paper, we introduce a Bayesian learning model to
    understand the behavior of Large Language Models (LLMs). We
    explore the optimization metric of LLMs, which is based on
    predicting the next token, and develop a novel model grounded in
    this principle. Our approach involves constructing an ideal
    generative text model represented by a multinomial transition
    probability matrix with a prior, and we examine how LLMs
    approximate this matrix. We discuss the continuity of the mapping
    between embeddings and multinomial distributions, and present the
    Dirichlet approximation theorem to approximate any prior.
    Additionally, we demonstrate how text generation by LLMs aligns
    with Bayesian learning principles and delve into the implications
    for in-context learning, specifically explaining why in-context
    learning emerges in larger models where prompts are considered as
    samples to be updated. Our findings indicate that the behavior of
    LLMs is consistent with Bayesian Learning, offering new insights
    into their functioning and potential applications.

Comments:    12 pages, 6 figures
Subjects:    Machine Learning (cs.LG); Artificial Intelligence
             (cs.AI)
ACM classes: I.2.7
Cite as:     arXiv:2402.03175 [cs.LG]
             (or arXiv:2402.03175v1 [cs.LG] for this version)
             https://doi.org/10.48550/arXiv.2402.03175
             Focus to learn more
             arXiv-issued DOI via DataCite

Submission history

From: Vishal Misra [view email]
[v1] Mon, 5 Feb 2024 16:42:10 UTC (305 KB)
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