… In order to state the problem more precisely, we need to describe the class of manifolds within
which we will search for the existence of a manifold which satisfies the manifold hypothesis…

… Manifold Learning can be loosely defined to be a collection … that this hypothesis (henceforth
called the manifold hypothesis) … manifold hypothesis, (assuming the decision boundary is a …

… explanation for why the Manifold Hypothesis seems to hold in so … manifold structure hides in
the data and how the manifold … explore manifold hypotheses grounded in a statistical model. …

… A main appeal of the manifold hypothesis is its broad potential for the analysis and … We
believe that it will be interesting to explore the connections between the manifold hypothesis and …

This thesis questions whether the positive manifold effect, first observed by Spearman (1925)
is equally influential across samples differing in intelligence level and age. In particular, the …

… we propose a heuristic framework for testing a multi-manifold hypothesis on real-world data
… -manifold whose dimensional components fit the partitions. Finally, we compute test statistics …

… In recent years there has been increased interest in understanding the interplay between
deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses …

… ial robustness using the manifold hypothesis. This framework … Our method combines
manifold learning with variational … In addition, our method can also serve as a test-time defense …

… We show that the manifold hypothesis on its own does not guarantee learnability. In particular,
we give hardness results for a class of low-dimensional manifolds in the statistical query (…

… The shared manifold hypothesis of intersubjectivity provides a general hypothesis that can
be empirically tested at multiple levels both in healthy and psychotic individuals. A related …