Augmenting Flexibility: Mutual Inhibition Between Inhibitory Neurons Expands Functional Diversity

Abstract

One of the most intriguing observations of recurrent neural circuits is their flexibility. Seemingly, this flexibility extends far beyond the ability to learn, but includes the ability to use learned procedures to respond to novel situations. Here, we report that this flexibility arises from the synergistic interplay between recurrent mutual excitation and recurrent mutual inhibition. Specifically, we show that mutual inhibition is critical in expanding the functionality of the circuit, far beyond what feedback inhibition alone can accomplish. By taking advantage of dynamical systems theory and bifurcation analysis, we show mutual inhibition doubles the number of cusp bifurcations in the system in small neural circuits. As a concrete example, we build a simulation model of a class of functional motifs we call Coupled Recurrent inhibitory and Recurrent excitatory Loops (CRIRELs). These CRIRELs have the advantage of being multi-functional, performing a plethora of functions, including decisions, switches, toggles, central pattern generators, depending solely on the input type. We then use bifurcation theory to show how mutual inhibition gives rise to this broad repertoire of possible functions. Finally, we demonstrate how this trend also holds for larger networks, and how mutual inhibition greatly expands the amount of information a recurrent network can hold.

Hyper-Flexible Neural Networks: Rapidly Switching between Logic Operations in a Compact 4-Neuron Circuit

“…Finally, we showed that the flexible gate switching can be used to create a 4-bit ripple carry adder. This is in line with previous research that has shown that recurrent neural networks are more flexible than their feedforward counterparts [38]. Specifically, this study takes advantage of a nearby cusp bifurcation [37].…”

“…To examine flexibility in small neural networks, we start with a CRIREL microcircuit [Fig 1a] [38]. This microcircuit is simultaneously near two cusp bifurcations [Fig 1b], and as such is capable of a simple two “bit” version of working memory [Fig 1b-c].…”

“…Being near the cusp of state changes allows the network to rapidly switch to qualitatively different dynamics upon manipulation of certain control parameters. However, while several studies have attempted to understand how bifurcations aid flexibility [39,38,4], it is still unclear how the nervous system can control networks near such complicated bifurcation structures without altering synaptic weights.…”

“…Moreover, it is proposed that this is a consequence of the network being near multiple bifurcations, i.e. at a position in which state changes are easy to induce [26, 34, 35, 36, 37, 38]. Being near the cusp of state changes allows the network to rapidly switch to qualitatively different dynamics upon manipulation of certain control parameters.…”

“…26.574759 doi: bioRxiv preprint recurrently connected excitatory pair and a recurrently connected inhibitory pair, where these pairs are then weakly coupled with one another. We showed that CRIRELs are flexible because we can control an underlying double cusp bifurcation present in the network [37,40,38], which allows for new stable or unstable states to emerge as control parameters (in this case, synaptic weights) are varied. However, synaptic weights are not the only controllable parameters, and here we demonstrate how varying bias currents (baseline activity level, implemented as a constant background input current) and input, while keeping synaptic weights fixed, also induces bifurcations and results in flexibility.…”