Multiple bumps can enhance robustness to noise in continuous attractor networks
Fig 2
Bump formation in a ring attractor network.
(A) Network schematic with populations L and R and locally inhibitory connectivity W. (B and C) Networks with 200 neurons and 3 bumps. (B) Connectivity weights for a neuron at the origin. The inhibition distance is l = 29 and the connectivity shift is ξ = 2. (C) Steady-state synaptic inputs. Curves for both populations lie over each other. With a ReLU activation function, the firing rates follow the solid portions of the colored lines and are 0 over the dashed portions. The bump distance is λ = 200/3. Thick gray line indicates Eq 4. (D and E) Networks with 500 neurons. (D) More bumps and shorter bump distances are produced by smaller inhibition distances. Points indicate data from 10 replicate simulations. Line indicates Eq 5. (E) The inhibition distance l = 55 corresponds to the black point in D with λ = 125 and M = 4. These values also minimize the Lyapunov functional (Eq 6), which varies smoothly across λ for infinite networks (line) and takes discrete values for finite networks (points). (F) The scaled bump shape remains invariant across network sizes and bump numbers, accomplished by rescaling connectivity strengths according to Eq 7. Curves for different parameters lie over one another.