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In this work, we investigate how feedforward LLMs solve two-hop factual recall tasks, which can be expressed compositionally as $g(f(x))$. We first confirm that modern LLMs continue to suffer from the \"compositionality gap\", i.e. their ability to compute both $z = f(x)$ and $y = g(z)$ does not entail their ability to compute the composition $y = g(f(x))$. We then decode residual stream representations and identify two processing mechanisms: one which solves tasks $\\textit{compositionally}$, computing $f(x)$ along the way to $g(f(x))$, and one which solves them $\\textit{directly}$, without any detectable signature of the intermediate variable $f(x)$. 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