(a) Schematic of circuit involving VIP, SST, PV, and PYR groups of neurons. When VIP are silent, PYR are self-excitatory, while SST and PV inhibit PYR. When VIP are active, they inhibit the PYR while also creating a disinhibitory motif given by VIP-SST-PYR. The potential connection from PYR to VIP explored in this article is marked with a dotted arrow. (b) Processing of two input types (e.g., images, videos) happens using two separate networks for each type of input, each having $N$ units with $2N2$ weights in total to learn. (c) Processing of two input types can be done with one circuit: a switching circuit with $N$ units adapted to one of the contexts and $M$ switching units that turn on when the other context is presented. We may want $M<<N$⁠, with $N2+2NM$ connections to learn (assuming switching units are not interconnected). When the number of switching units required in a switching circuit is small, fewer connections need to be learned; more specifically, if $M<N/2⇒N2+2MN<2N2$⁠. This generalizes well to a range of circuits, including in the case of sparse connectivities, as often presented throughout the article.