Linear Representation Transferability Hypothesis: Leveraging Small Models to Steer Large Models

TL;DR

This paper proposes the Linear Representation Transferability hypothesis, suggesting that affine transformations can align hidden representations across models of different sizes, enabling small models to steer larger models effectively.

Contribution

It introduces the LRT hypothesis and demonstrates that affine mappings can transfer steering behaviors from small to large models.

Findings

Affine mappings can preserve steering behaviors across models

Small models' representations can guide large models

Representation alignment across scales is feasible

Abstract

It has been hypothesized that neural networks with similar architectures trained on similar data learn shared representations relevant to the learning task. We build on this idea by extending the conceptual framework where representations learned across models trained on the same data can be expressed as linear combinations of a \emph{universal} set of basis features. These basis features underlie the learning task itself and remain consistent across models, regardless of scale. From this framework, we propose the \textbf{Linear Representation Transferability (LRT)} Hypothesis -- that there exists an affine transformation between the representation spaces of different models. To test this hypothesis, we learn affine mappings between the hidden states of models of different sizes and evaluate whether steering vectors -- directions in hidden state space associated with specific model behaviors -- retain their semantic effect when transferred from small to large language models using the learned mappings. We find strong empirical evidence that such affine mappings can preserve steering behaviors. These findings suggest that representations learned by small models can be used to guide the behavior of large models, and that the LRT hypothesis may be a promising direction on understanding representation alignment across model scales.