Towards a Learning Theory of Representation Alignment
This work addresses the theoretical underpinnings of representation alignment for AI researchers, but it is incremental as it builds on existing empirical analyses.
The paper tackles the problem of understanding representation alignment in AI models by proposing a learning-theoretic perspective, relating stitching properties to kernel alignment as a foundational step.
It has recently been argued that AI models' representations are becoming aligned as their scale and performance increase. Empirical analyses have been designed to support this idea and conjecture the possible alignment of different representations toward a shared statistical model of reality. In this paper, we propose a learning-theoretic perspective to representation alignment. First, we review and connect different notions of alignment based on metric, probabilistic, and spectral ideas. Then, we focus on stitching, a particular approach to understanding the interplay between different representations in the context of a task. Our main contribution here is relating properties of stitching to the kernel alignment of the underlying representation. Our results can be seen as a first step toward casting representation alignment as a learning-theoretic problem.