Extended Data Fig. 6: Model identifiability for the CAN model.
a, Schematics of the model, similar to Fig. 4a. GC modules receive input from a LM that receives both internal input (Iint) from GCs and external input (Iext) from visual stimuli. The synaptic weights from GC to LM undergo Hebbian plasticity (‘+’) and undergo learning both in the presence of Iext mimicking conditions in NTS and in its absence mimicking conditions in MNAV. b, Learning of GC to LM connections in the presence of Iext with a specific periodicity and 4 different phases (i.e., 4 different model simulations). Left, synaptic weights from all neurons in all GC modules (m1, m2, m3, m4) are initially random. Middle, after learning, synaptic weights of those GC cells whose periodicity and phase match Iext (middle) strengthens. Right, tests of the model with landmark placed at 8 different phases. Learned landmark phase, computed as the phase of the GC neuron with maximum weight to the LM neuron, plotted as a function of the true landmark phase for the appropriate module (red) and all other modules (grey). c, Learning in a new instantiation of the model with 20 modules. Left, in the presence of Iext with a specific periodicity and phase (black circle), the model learns the correct phase and periodicity. Right, robustness of learning relative to landmark periodicity. The model learns to associate the module with the correct periodicity for a wide range of scales. d, Left, ACG of average unit activation (top) and ACG of Fano factor (bottom) of all units in the model under noisy velocity (average velocity: 42 a.u.). Middle, average ACG across all units for a range of velocity (red: fastest; black: slowest). Right, periodicity of unit activation and Fano factor both scale with the velocity input. e, Left, model simulations with (red) and without landmarks (black) under different levels of noise (Weber fraction, wm=0.2 and 0.5; wm=0.8 in Fig. 4c,d; avg. velocity: 42 a.u.). Dotted lines denote the distance traversed in 650 ms and its multiples. Arrows point to locations of endogenous resets in the network dynamics. Middle, bootstrapped standard deviation of temporal distance versus mean temporal distance at corresponding noise levels. Right, mean-matched temporal distances were achieved by adjusting velocity input to the models.
