Fig. 1: Representational dimensionality, dynamics, and selectivity.

Schematic illustration of representational dimensionality, dynamics, and selectivity of the conjunctive control representations. Each panel plots the response of a toy population of three units to input conditions varying in shape (square or circle) and color (red or black). Axes represent the firing rates of single units, collectively defining a neural activity space for the population. Each point within this activity space represents the population response to a given input (identified by colored shapes). Distance between points reflects how distinct responses are, and the jittered cloud of points reflects the trial-by-trial variability in responses to a given input. A The geometric format of the population neural responses is defined by response patterns arranged in 3 dimensions. A linear readout is implemented by a decision hyperplane (yellow) that divides the readout subspace into different classes (e.g., different shapes of inputs). The high-dimensional representation (traced by solid black lines), where no cluster of responses are aligned to each other, allows a wider variety of input conditions to be linearly separable. In addition, responses projected to a readout subspace defined by a linear hyperplane tend to dissociate input conditions (e.g., red-square and black-square) that are on the same side of the decision boundary, increasing the separability of neural responses overall. B Due to the time-varying nature of neural activity, the neural state space is changing and reshaping its underlying geometry over time. The dynamic neural trajectories potentially require changes in the weights for optimal linear hyperplanes for downstream readouts. C Units within the population show a heterogeneous turning profile or nonlinear mixed selectivity. To illustrate, the tuning profile for one unit (r₂) is plotted along the corresponding axis. The bars plot the activity of r₂ to each of the four conditions of input and depict a non-linear mixed selective pattern. Note that similar geometric properties are expected at the level of a single unit (i.e., mixed-selectivity) or population of neurons (i.e., integrative subspaces). The event-file representations could be conceptualized as one form of mixed selectivity where a unit or groups of units are exclusively tuned to a specific combination of task-critical factors more than other pairs.