  Echoing recent calls to counter reliability and robustness concerns in
machine learning via multiverse analysis, we present PRESTO, a principled
framework for mapping the multiverse of machine-learning models that rely on
latent representations. Although such models enjoy widespread adoption, the
variability in their embeddings remains poorly understood, resulting in
unnecessary complexity and untrustworthy representations. Our framework uses
persistent homology to characterize the latent spaces arising from different
combinations of diverse machine-learning methods, (hyper)parameter
configurations, and datasets, allowing us to measure their pairwise
(dis)similarity and statistically reason about their distributions. As we
demonstrate both theoretically and empirically, our pipeline preserves
desirable properties of collections of latent representations, and it can be
leveraged to perform sensitivity analysis, detect anomalous embeddings, or
efficiently and effectively navigate hyperparameter search spaces.
