Density estimation with LLMs: a geometric investigation of in-context learning trajectories
File(s)
Accepted version
Author(s)
Liu, Toni
Boulle, Nicolas
Sarfati, Raphael
Earls, Christopher
Type
Conference Paper
Abstract
Large language models (LLMs) demonstrate remarkable emergent abilities to perform in-context learning across various tasks, including time series forecasting. This work investigates LLMs’ ability to estimate probability density functions (PDFs) from data observed in-context; such density estimation (DE) is a fundamental task underlying many probabilistic modeling problems. We leverage the
Intensive Principal Component Analysis (InPCA) to visualize and analyze the in-context learning dynamics of LLaMA-2 models. Our main finding is that these LLMs all follow similar learning trajectories in a low-dimensional InPCA space,
which are distinct from those of traditional density estimation methods like histograms and Gaussian kernel density estimation (KDE). We interpret the LLaMA
in-context DE process as a KDE with an adaptive kernel width and shape. This custom kernel model captures a significant portion of LLaMA’s behavior despite having only two parameters. We further speculate on why LLaMA’s kernel width and shape differs from classical algorithms, providing insights into the mechanism of in-context probabilistic reasoning in LLMs.
Intensive Principal Component Analysis (InPCA) to visualize and analyze the in-context learning dynamics of LLaMA-2 models. Our main finding is that these LLMs all follow similar learning trajectories in a low-dimensional InPCA space,
which are distinct from those of traditional density estimation methods like histograms and Gaussian kernel density estimation (KDE). We interpret the LLaMA
in-context DE process as a KDE with an adaptive kernel width and shape. This custom kernel model captures a significant portion of LLaMA’s behavior despite having only two parameters. We further speculate on why LLaMA’s kernel width and shape differs from classical algorithms, providing insights into the mechanism of in-context probabilistic reasoning in LLMs.
Date Acceptance
2025-01-22
Publisher
Curran Associates, Inc.
Copyright Statement
Subject to copyright. This paper is embargoed until publication.
Source
International Conference on Learning Representations (ICLR 2025)
Publication Status
Accepted
Start Date
2025-04-24
Finish Date
2025-04-28
Coverage Spatial
Singapore