A novel approach to the empirical characterization of learning in biological systems

Learning to execute precise, yet complex, motor actions through practice is a trait shared by most organisms. Here we develop a novel experimental approach for the comprehensive investigation and characterization of the learning dynamics of practiced motion. Following the dynamical systems framework, we consider a high-dimensional behavioral space in which a trial-by-trial sequence of motor outputs defines a trajectory that converges to a fixed point - the desired motor output. In this scenario, details of the internal dynamics and the trial-by-trial learning mechanism cannot be disentangled from behavioral noise for nonlinear systems or even well estimated for linear systems with many parameters. To overcome this problem, we introduce a novel approach: the sporadic application of systematic target perturbations that span the behavioral space and allow us to estimate the linearized dynamics in the vicinity of the fixed point. The steady-state Lyapunov equation then allows us to identify the noise covariance. We illustrate the method by analyzing sequence-generating neural networks with either intrinsic or extrinsic noise, at time resolutions that span from spike timing to spiking rates. We demonstrate the utility of our approach in experimentally plausible and realizable settings and show that this method can fully characterize the linearized between-trials learning dynamics as well as extract meaningful internal properties of the unknown mechanism that drives the motor output within each trial. We then illustrate how the approach can be extended to nonlinear learning dynamics through a flexible choice of the basis and magnitude of perturbations.