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Recent studies have suggested a processing framework for multilingual inputs in decoder-based LLMs: early layers convert inputs into English-centric and language-agnostic representations; middle layers perform reasoning within an English-centric subspace; and final layers generate outputs by transforming these representations back into language-specific subspaces. However, the internal dynamics of such transformation and the underlying mechanism remain underexplored. Towards a deeper understanding of this framework, we propose and empirically validate The Transfer Neurons Hypothesis: certain neurons in the MLP module are responsible for transferring representations between language-specific subspaces and a shared semantic subspace. Furthermore, we show that one function of language-specific neurons, as identified in recent studies, is to facilitate movement between subspaces. Finally, we show that transfer neurons are critical for reasoning in multilingual LLMs.