Multiple bumps can enhance robustness to noise in continuous attractor networks

A central function of continuous attractor networks is encoding coordinates and accurately updating their values through path integration. To do so, these networks produce localized bumps of activity that move coherently in response to velocity inputs. In the brain, continuous attractors are believed to underlie grid cells and head direction cells, which maintain periodic representations of position and orientation, respectively. These representations can be achieved with any number of activity bumps, and the consequences of having more or fewer bumps are unclear. We address this knowledge gap by constructing 1D ring attractor networks with different bump numbers and characterizing their responses to three types of noise: fluctuating inputs, spiking noise, and deviations in connectivity away from ideal attractor configurations. Across all three types, networks with more bumps experience less noise-driven deviations in bump motion. This translates to more robust encodings of linear coordinates, like position, assuming that each neuron represents a fixed length no matter the bump number. Alternatively, we consider encoding a circular coordinate, like orientation, such that the network distance between adjacent bumps always maps onto 360 degrees. Under this mapping, bump number does not significantly affect the amount of error in the coordinate readout. Our simulation results are intuitively explained and quantitatively matched by a unified theory for path integration and noise in multi-bump networks. Thus, to suppress the effects of biologically relevant noise, continuous attractor networks can employ more bumps when encoding linear coordinates; this advantage disappears when encoding circular coordinates. Our findings provide motivation for multiple bumps in the mammalian grid network.Author summary: Our brains maintain an internal sense of location and direction so we can, for example, find our way to the door if the lights go off. A class of neural circuits called continuous attractor networks is believed to be responsible for this ability. These circuits must be resilient against the myriad forms of imperfections and random fluctuations present in the brain, which can degrade the accuracy of their encoded information. We have discovered a new way in which continuous attractor networks can improve their robustness to noise: they should distribute their activity among multiple regions in the network, called bumps, instead of concentrating it in a single bump. Bump number is a fundamental feature of continuous attractor networks, but its connection to error suppression has never been appreciated. A recent experiment in rodents suggests that one such network indeed contains multiple regions of activity; our finding provides motivation for why such a configuration may have been evolved.