  Most works in learning with differential privacy (DP) have focused on the
setting where each user has a single sample. In this work, we consider the
setting where each user holds $m$ samples and the privacy protection is
enforced at the level of each user's data. We show that, in this setting, we
may learn with a much fewer number of users. Specifically, we show that, as
long as each user receives sufficiently many samples, we can learn any
privately learnable class via an $(\epsilon, \delta)$-DP algorithm using only
$O(\log(1/\delta)/\epsilon)$ users. For $\epsilon$-DP algorithms, we show that
we can learn using only $O_{\epsilon}(d)$ users even in the local model, where
$d$ is the probabilistic representation dimension. In both cases, we show a
nearly-matching lower bound on the number of users required.
  A crucial component of our results is a generalization of global stability
[Bun et al., FOCS 2020] that allows the use of public randomness. Under this
relaxed notion, we employ a correlated sampling strategy to show that the
global stability can be boosted to be arbitrarily close to one, at a polynomial
expense in the number of samples.
