Exploring neural manifolds across a wide range of intrinsic dimensions

Recent technical breakthroughs have enabled a rapid surge in the number of neurons that can be simultaneously recorded, calling for the development of robust methods to investigate neural activity at a population level. In this context, it is becoming increasingly important to characterize the neural activity manifold, the set of configurations visited by the network within the space defined by the instantaneous firing rates of all neurons. The intrinsic dimension (ID) of the manifold is a key parameter allowing to relate neural trajectories with the ongoing network computations. While several studies suggested that the ID may be typically low in neural manifolds, contrasting findings have disputed this statement, leading to a wide debate. Part of the disagreement may stem from the lack of a shared and robust methodology to measure the ID. In the case of curvature, linear methods tend to overestimate the ID; in the case of undersampling, nonlinear methods tend underestimate it. Here we show that adapting the full correlation integral (FCI) method yields an estimator that is robust to both curvature and undersampling. We tested our metric on artificial data, including neural trajectories generated recurrent neural networks (RNNs) performing simple tasks and a benchmark dataset consisting of non-linearly embedded high-dimensional data. Our methodology provides a reliable and versatile tool for the analysis of neural geometry.