Leaving the Cave by Breaking the Symmetry: Identifiable Structure Can Enable Cross-Lingual Generalization
Frederick Riemenschneider, Anette Frank
Why do multilingual language models generalize across languages even without shared vocabulary? The Platonic Representation Hypothesis posits that models trained on different data, objectives, and modalities converge toward a shared statistical model of reality. Extending this intuition to representations inside a single multilingual model, we propose the Relational Identifiability Hypothesis: relations in a shared world can promote entity alignment by ruling out alternative cross-lingual correspondences, making corresponding entities more likely to become directly readable without an additional transformation. We test this hypothesis in a controlled bilingual Transformer whose two token-disjoint languages describe the same modular-arithmetic world. We find that the languages can develop a shared answer subspace without aligning corresponding numbers. Cross-lingual alignment emerges selectively when the available relations constrain number correspondences: subtraction makes zero task-level identifiable, inducing selective alignment, while an order-sensitive operation produces broad alignment across numbers. These patterns predict success in zero-shot cross-lingual transfer. Together, our results show that relational structure in a shared world can promote entity alignment and enable transfer.
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