Population coding

Representation through the joint activity of multiple neurons. Information can reside in relative activity patterns even when the overall mean activity changes little. Neural decoding tests whether recorded patterns carry accessible information under a specified analysis.

Statistical dependence between neural responses remaining after the modeled task-related mean has been removed. Residual dependence can reflect shared state or omitted task variables as well as biological noise, so its interpretation depends on the conditioning model.

Coordinates describing the joint activity of a neural population, often using one coordinate per cell or fitted latent variable. A trajectory connects states over time. A useful reduced description requires evidence that it retains the neural and behavioral properties relevant to the intended claim.

In the observation model $y=Cz+b$, let $Q$ be an orthogonal matrix. Replacing $z$ by $Qz$ and $C$ by $C{Q}^T$ leaves $y$ unchanged because $Q^{T}Q=I$. Thus reconstruction alone does not give each latent axis a unique biological meaning. A particular stochastic model can restrict this symmetry through its prior and parameter constraints; the algebra does not claim every fitted latent model has every rotational ambiguity.

A proposed lower-dimensional set around which recorded population states are organized. The estimated dimension depends on sampling, noise, preprocessing and the scale of variation. A visually smooth embedding is not by itself proof of an intrinsic biological manifold.

The evolution of a population representation over time. A trajectory estimated after trial averaging or strong smoothing can differ from every individual-trial trajectory; this distinction matters for claims about neural dynamics.