  To gain insight into the mechanisms behind machine learning methods, it is
crucial to establish connections among the features describing data points.
However, these correlations often exhibit a high-dimensional and strongly
nonlinear nature, which makes them challenging to detect using standard
methods. This paper exploits the entanglement between intrinsic dimensionality
and correlation to propose a metric that quantifies the (potentially nonlinear)
correlation between high-dimensional manifolds. We first validate our method on
synthetic data in controlled environments, showcasing its advantages and
drawbacks compared to existing techniques. Subsequently, we extend our analysis
to large-scale applications in neural network representations. Specifically, we
focus on latent representations of multimodal data, uncovering clear
correlations between paired visual and textual embeddings, whereas existing
methods struggle significantly in detecting similarity. Our results indicate
the presence of highly nonlinear correlation patterns between latent manifolds.
