Algorithms to Map Neural Activity to Behavior

Quantitative science has long been dominated by physics, which aims to express relationships among natural variables through equations. These equations ideally require linearity, decomposability, and Gaussian noise for analytical solutions. However, such assumptions break down for highly nonlinear systems, where traditional physics-based approaches have struggled. In contrast, Deep Learning has shown surprising success in capturing nonlinear mappings—but at the cost of explainability due to its “black box” nature. Neural activity is profoundly nonlinear. To address this with interpretability, we introduce a framework based on the generalized Takens theorem from dynamical systems theory. It enables data-driven embeddings of time series on low-dimensional manifolds that map neural activity to behavior. This allows for prediction, causal inference at scale, simulation, and guarantees of explainability and testability. We demonstrate several use cases in animal and human systems neuroscience that effectively simulate neural and behavioral dynamics—akin to single-behavior brain downloads.