Neural trajectory

A neural trajectory is the path traced out over time by the population state — either the raw activity vector or, more usefully, the latent state — as a curve in a low-dimensional space. Points along the curve are successive moments of the behaviour, and geometric features of the curve (its speed, curvature, how trajectories for different conditions separate or run parallel) become the primary description of what the population is doing. This is the shift from asking what each neuron encodes to asking how the population state moves.

Two distinctions matter in practice. Condition-averaged trajectories are smooth and easy to interpret but hide single-trial variability; single-trial trajectories (from methods like GPFA or LFADS) are noisier but are what a real-time decoder must actually track. And because latent coordinates are only defined up to a transformation, the shape of a trajectory is meaningful within a fixed embedding but its absolute axes are not, so cross-session or cross-subject comparisons require alignment before the geometry can be compared.