Towards Understanding Steering Strength

TL;DR

This paper provides the first theoretical analysis of steering strength in large language models, revealing complex effects on model behavior and validating predictions across various models.

Contribution

It introduces a novel theoretical framework for understanding how steering strength influences language model outputs, highlighting non-monotonic effects.

Findings

Steering strength affects next token probability and concept presence.

Non-monotonic effects observed with varying steering strength.

Theoretical laws accurately predict empirical behaviors.

Abstract

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.