Figure 1.

Representational geometries and their reflection in distance matrices. (A) Illustration of ten hypothetical representational geometries for brain regions (numbered 1–10). Each dot corresponds to the representation of a particular piece of content (e.g., a visual object). The space in which the dots are placed is the space of representational patterns (illustrated as two-dimensional, but high-dimensional in reality). The halo regions around the dots indicate the margin of error; dots with overlapping error halos are indistinguishable. The items fall into two categories (dark or light), or in the case of geometry 10, on a continuous manifold (shades of gray). (1) No item is distinct from any other item. (2) Most items are distinctly represented but the categories cannot be separated by any simple boundary. (3) Only the light items are distinctly represented and they are separable from the dark items by a quadratic boundary. (4) Dark and light items are linearly separable and arranged along parallel lines with pairs of dark and light dots matched up across the boundary. (5) The items form a single cluster but the categories are linearly separable. (6) The items form two category clusters that are linearly separable and within which all items are distinct. (7) Like the previous case, but the items in the dark category are indistinguishable. (8) Like the previous case, but only the category distinction is represented; items within each category are indistinguishable from each other. (9) The dark items are indistinguishable and located among the distinctly represented light items on a circle. (10) Items fall on two manifolds that closely follow each other, with pairs of items matched up across them. (B) Representational distance matrix for each of the ten geometries (in the corresponding panel location). Distances are color-coded from blue (items indistinguishable) to red (items widely separated). Each matrix is indexed vertically (from the top down) and horizontally (from left to right) by the items as illustrated in the lower left panel. Only geometry 10 (lower right) has a different item set, and the upper left quadrant corresponds to the front manifold and the lower right quadrant to the back manifold. See Box 2 for actual brain representations exhibiting some of the geometric features illustrated here.