Linear Representation Transferability Hypothesis: Leveraging Small Models to Steer Large Models
This work addresses the challenge of understanding and leveraging representation alignment across model scales, which could enable more efficient steering of large models, though it appears incremental as it builds on existing hypotheses about shared representations.
The paper tackles the problem of aligning representations across neural networks of different scales by proposing the Linear Representation Transferability (LRT) Hypothesis, which posits an affine transformation between representation spaces, and finds strong empirical evidence that steering vectors from small models can guide large model behaviors when transferred via learned mappings.
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.