  Researchers often hold the belief that random forests are "the cure to the
world's ills" (Bickel, 2010). But how exactly do they achieve this? Focused on
the recently introduced causal forests (Athey and Imbens, 2016; Wager and
Athey, 2018), this manuscript aims to contribute to an ongoing research trend
towards answering this question, proving that causal forests can adapt to the
unknown covariate manifold structure. In particular, our analysis shows that a
causal forest estimator can achieve the optimal rate of convergence for
estimating the conditional average treatment effect, with the covariate
dimension automatically replaced by the manifold dimension. These findings
align with analogous observations in the realm of deep learning and resonate
with the insights presented in Peter Bickel's 2004 Rietz lecture.
