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.

探索了机器学习方法背后的机制，利用内在维度与相关性之间的纠缠提出了一种度量标准，用于量化高维流形之间的相关性。验证了方法在合成数据上的优势和缺点，并在神经网络表示中将分析扩展到大规模应用，揭示了多模态数据的潜在表示之间明显的关联，而现有方法在检测相似性方面存在显著困难。研究结果表明了潜在流形之间高度非线性的相关性模式的存在。