  Recent work has established that the conditional mutual information (CMI)
framework of Steinke and Zakynthinou (2020) is expressive enough to capture
generalization guarantees in terms of algorithmic stability, VC dimension, and
related complexity measures for conventional learning (Harutyunyan et al.,
2021, Haghifam et al., 2021). Hence, it provides a unified method for
establishing generalization bounds. In meta learning, there has so far been a
divide between information-theoretic results and results from classical
learning theory. In this work, we take a first step toward bridging this
divide. Specifically, we present novel generalization bounds for meta learning
in terms of the evaluated CMI (e-CMI). To demonstrate the expressiveness of the
e-CMI framework, we apply our bounds to a representation learning setting, with
$n$ samples from $\hat n$ tasks parameterized by functions of the form $f_i
\circ h$. Here, each $f_i \in \mathcal F$ is a task-specific function, and $h
\in \mathcal H$ is the shared representation. For this setup, we show that the
e-CMI framework yields a bound that scales as $\sqrt{ \mathcal C(\mathcal
H)/(n\hat n) + \mathcal C(\mathcal F)/n} $, where $\mathcal C(\cdot)$ denotes a
complexity measure of the hypothesis class. This scaling behavior coincides
with the one reported in Tripuraneni et al. (2020) using Gaussian complexity.
