Figure 1: Optimal representations are formed through an information bottleneck.

(a) Consider the task $Y$ of discerning whether the image is of a dog. Images to the right have less information than the original image ($I(\mathbf{Z};\mathbf{X})$ is smaller) but still contain approximately the same amount of information, $I(\mathbf{Z};Y)$ to perform the task: “is this a dog?” (b) The information bottleneck trades off minimality, $I(\mathbf{Z};\mathbf{X})$ as small as possible, with sufficiency, $I(\mathbf{Z};Y)\approx I(\mathbf{X};Y)$. (c) Checkerboard task. The monkey reaches to the target whose color matches the checkerboard dominant color. Because there are two equally likely target configurations where the color of the left and right targets are swapped, this task unmixes the color and direction choice. (d) A minimal sufficient representation of this task is to only retain the direction decision, in this case, reach left. A cortical information bottleneck should therefore only find direction choice information in premotor and motor output areas.