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This emerging compatibility between independently trained models introduces new opportunities for cross-model alignment to downstream objectives. Moreover, this capability unlocks new potential application domains, such as settings where security, privacy, or competitive constraints prohibit direct data or model sharing. In this work, we investigate the extent to which representational convergence enables practical linear alignment between large language models. Specifically, we learn affine transformations between the final hidden states of independent models and empirically evaluate these mappings across text generation, embedding classification, and out-of-distribution detection. 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