Abstract

Understanding complex dynamical systems, such as the brain, is challenging due to the high dimensionality of the data and complex interactions between components. Even a complete characterisation of cause-effect relationships between variables may not improve our understanding due to the sheer complexity. Conventional dimensionality reduction techniques such as PCA and t-SNE are unsupervised and generally aim to optimise reconstruction quality. This is limiting when we are interested in understanding the dynamics of a specific target variable. Here, we introduce BunDLe-Net, a manifold-learning algorithm that effectively preserves relevant information while abstracting away details that are irrelevant to the target variable. We apply it to neuronal data from the roundworm C. elegans. BunDLe-Net reveals clear orbit-like trajectories which are recurrent and structured. I like to think of them as ’thought trajectories' since they are derived from neuronal data. From these trajectories, one can directly read off information about decision-making, uncertainty, future dynamics and behavioural patterns. It is a powerful visualisation tool for high-dimensional time-series data in the context of a target variable, outperforming conventional and state-of-the-art methods.