Towards a Learning Theory of Representation Alignment

• URL: http://arxiv.org/abs/2502.14047v1
• Date: Wed, 19 Feb 2025 19:09:14 GMT
• Title: Towards a Learning Theory of Representation Alignment
• Authors: Francesco Insulla, Shuo Huang, Lorenzo Rosasco,
• Abstract summary: We propose a learning-theoretic perspective to representation alignment.<n>Our results can be seen as a first step toward casting representation alignment as a learning-theoretic problem.
• Score: 12.166663160280056
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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