Neural Embedding Alignment Reveals Nonlinear Latent Transformations across Brain Regions

Latent variable models are powerful tools for characterizing high-dimensional neural population activity, and recent work has extended these models to multi-region settings. However, most existing approaches assume linear relationships between populations, limiting their ability to capture the complex, nonlinear mappings that may exist between brain regions. Nonlinear methods, while more flexible, often yield latent spaces whose structure is not uniquely determined, complicating cross-region comparisons.We introduce a nonlinear variational framework with an alignment objective inspired by stochastic neighbor embedding. Our method enables explicit control over the degree of alignment between latent spaces via a tunable hyperparameter, allowing representations to remain independent or become aligned to facilitate interpretability. We demonstrate the approach on both synthetic data from a four-layer deep neural network and multi-region neural recordings from mouse visual cortex. Across both settings, the method successfully aligns latent spaces and reveals how manifolds transform across layers or brain regions, providing a flexible tool for probing neural information transformations.