Multiple bumps can enhance robustness to noise in continuous attractor networks
Fig 6
Mutual information between neural activity and physical coordinates with input noise of magnitude σ = 0.5.
(A) To compute mutual information, we initialize replicate simulations without input drive at different coordinate values (thick black lines) and record the final neural activities (thin colored lines). The physical coordinate can be linear or circular and its range can be narrow or wide; here, we illustrate two possibilities for networks with 600 neurons and 3 bumps. (B and C) Mutual information between physical coordinate and single-neuron activity under narrow coordinate ranges. (B) Information increases with bump number for linear coordinates and remains largely constant for circular coordinates. Networks with 600 neurons. (C) Information decreases with network size for linear coordinates and increases for circular coordinates. Networks with 3 bumps. (D and E) Mutual information between physical coordinate and single-neuron activity under wide coordinate ranges. The trends in B and C are preserved for circular coordinates. They are also preserved for linear coordinates, except for the shaded regions in which the coordinate range exceeds the bump distance. (F) Coarse local cues are active over different quadrants of the wide coordinate ranges. (G and H) Mutual information between physical coordinate and the joint activities of a single neuron with the four cues in F under wide coordinate ranges. The trends in B and C are preserved for both linear and circular coordinates. Points indicate data from 96 replicate simulations at each coordinate value averaged over neurons and bars indicate bootstrapped standard errors of the mean. Cue icons adapted from Streamline Freemoji (CC BY license, https://www.streamlinehq.com/emojis/freebies-freemojis).