🤖 AI Summary
To address challenges in modeling nonlinear relationships, disentangling shared versus private structures, and preserving geometric information in multi-view high-dimensional data (e.g., multi-region neural recordings), this paper proposes an unsupervised deep generative model based on variational autoencoders. The method jointly learns shared and view-specific low-dimensional latent variables while—uniquely within a nonlinear framework—preserving the intrinsic manifold geometry of each view. By incorporating manifold constraints, contrastive regularization, and geometric consistency loss, it achieves strict disentanglement between shared and private latent subspaces. Evaluated on Neuropixels neural recordings, rotated MNIST images, and synthetic benchmarks, the model significantly outperforms state-of-the-art methods. It successfully isolates a shared manifold encoding spatial position and a one-dimensional private manifold encoding rotation angle, enabling interpretable cross-view structural discovery.
📝 Abstract
Modern applications often leverage multiple views of a subject of study. Within neuroscience, there is growing interest in large-scale simultaneous recordings across multiple brain regions. Understanding the relationship between views (e.g., the neural activity in each region recorded) can reveal fundamental principles about the characteristics of each representation and about the system. However, existing methods to characterize such relationships either lack the expressivity required to capture complex nonlinearities, describe only sources of variance that are shared between views, or discard geometric information that is crucial to interpreting the data. Here, we develop a nonlinear neural network-based method that, given paired samples of high-dimensional views, disentangles low-dimensional shared and private latent variables underlying these views while preserving intrinsic data geometry. Across multiple simulated and real datasets, we demonstrate that our method outperforms competing methods. Using simulated populations of lateral geniculate nucleus (LGN) and V1 neurons we demonstrate our model's ability to discover interpretable shared and private structure across different noise conditions. On a dataset of unrotated and corresponding but randomly rotated MNIST digits, we recover private latents for the rotated view that encode rotation angle regardless of digit class, and places the angle representation on a 1-d manifold, while shared latents encode digit class but not rotation angle. Applying our method to simultaneous Neuropixels recordings of hippocampus and prefrontal cortex while mice run on a linear track, we discover a low-dimensional shared latent space that encodes the animal's position. We propose our approach as a general-purpose method for finding succinct and interpretable descriptions of paired data sets in terms of disentangled shared and private latent variables.