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We posit two explanations for this phenomenon: pre-caching, in which off-diagonal gradient terms present during training result in the model computing features at $t$ irrelevant to the present inference task but useful for the future, and breadcrumbs, in which features most relevant to time step $t$ are already the same as those that would most benefit inference at time $t+\\tau$. We test these hypotheses by training language models without propagating gradients to past timesteps, a scheme we formalize as myopic training. In a constructed synthetic data setting, we find clear evidence for pre-caching. 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