Latent neural state

The latent neural state is the low-dimensional vector z_t whose evolution is taken to summarize the whole population at time t; each neuron's firing rate is modelled as a noisy function of z_t, usually linear (factor loadings) plus a nonlinearity or spiking observation model. It formalizes the manifold idea into an estimation problem: rather than track thousands of noisy spike counts, one infers the small latent vector that best explains them, using factor analysis, Gaussian-process factor analysis, or nonlinear sequential models such as LFADS. The latent state is the natural object for the dynamical-systems view, because dynamics are written as rules on z, not on individual rates.

It is important to keep the latent neural state distinct from the kinematic state estimated by a movement decoder. The kinematic state (position, velocity) is an externally defined quantity that the observation model maps onto neural activity; the latent neural state is an internal descriptor recovered from the neural activity itself and need not correspond to any single behavioural variable. Latent estimates are also model-dependent and rotation-ambiguous: without extra constraints the latent coordinates are identified only up to an invertible transformation, so comparisons across sessions or methods require explicit alignment.