Neural Manifold

Neural manifolds represent high-dimensional data as lower-dimensional geometric structures, aiming to capture the intrinsic relationships within complex datasets. Current research focuses on developing and analyzing neural network architectures, such as graph neural networks and Riemannian residual networks, that operate effectively on these manifolds, often leveraging techniques like variational autoencoders for dimensionality reduction and manifold construction. This approach improves the generalization and interpretability of machine learning models across diverse applications, including image classification, robotic control, and fMRI analysis, by exploiting the underlying geometric structure of the data.