Polynomial Regression as a Task for Understanding In-context Learning Through Finetuning and Alignment

TL;DR

This paper introduces univariate polynomial regression as a new, structured function class to better understand in-context learning, prompting, and alignment in transformer-based models, enabling clearer visualization and analysis.

Contribution

It proposes polynomial regression as a novel, structured function class for studying in-context learning, bridging the gap between simple models and complex neural architectures.

Findings

Polynomial regression allows visualization of in-context learning processes.

It provides insights into prompting and alignment mechanisms.

The approach facilitates understanding of model behavior with structured functions.

Abstract

Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or multi-layer-perceptrons lack the structure required to explore things like prompting and alignment within models capable of in-context-learning. We propose univariate polynomial regression as a function class that is just rich enough to study prompting and alignment, while allowing us to visualize and understand what is going on clearly.