Reliable neural manifold decoding using low-distortion alignment of tangent spaces

Since the advent of large-scale extracellular recordings in neuroscience and the widespread adoption of neural population frameworks, there is an increased need to achieve efficient decoding of task-relevant behavioral information from neural dynamics. The most prevalent methods to uncover task-related topologies in population dynamics, often approximated as neural manifolds, are linear dimensionality reduction methods such as principal component analysis (PCA). These techniques, however, find large-variance subspaces within which to embed neural manifolds and such embeddings do not necessarily provide the most informative means to decode behavioral metrics. On the other hand, nonlinear manifold learning techniques enable direct access to manifold geodesics, which may improve behavioral metric decoding or provide new analysis perspectives. Many manifold learning techniques, unfortunately, produce highly-distorted embeddings, which severely curtails their effectiveness for neuroscience applications. Optimization of these techniques for neural data presents its own challenges since neural data are often noisy, sparse, and nonhomogenous. To address this, we leverage recurrent neural network models (RNN), which can reliably replicate neural dynamics underlying several behaviors. We use RNNs to construct and control task-based manifolds with known dynamics, intrinsic dimensions, noise, sparsity, and density. Using these as a testbed, we present a manifold learning technique, Riemannian Alignment of Tangent Spaces (RATS), which efficiently constructs and aligns local views to obtain a global embedding. We demonstrate that RATS yields the lowest distortion embeddings when compared to several manifold learning techniques. This leads to improved decoding of behavioral metrics from noisy and sparse task-relevant manifolds underlying two sensorimotor tasks. Methods like RATS could help better decipher the elusive links between neural population dynamics and behavior, an issue that remains central to systems neuroscience.