Supplementary Figure 7: Inferring inputs from a chaotic data RNN with delta pulse inputs.

We tested the ability of LFADS to infer the input to a dynamical system, specifically chaotic data RNNs, as used in Supp. Fig. 3. During each trial, we perturbed the network by delivering a delta pulse at a random time t_pulse between 0.25s and 0.75s. The full trial length was 1s. This pulse affected the underlying rates produced by the data RNN, which subsequently affected the generated spike trains that were used as input to LFADS. To test the ability of LFADS to infer the timing of the input pulses, we allowed the LFADS model to infer a time-varying input (1-dimensional). We explored two levels of dynamical complexity in the data RNNs (see Online Methods), defined by two values, 1.5 and 2.5, of a hyper-parameter to the data RNN, γ. a-c γ = 1.5. This value of γ value produces “gentler" chaotic activity in the data RNN than the higher value. a. Example trial illustrating results from the γ = 1.5 chaotic data RNN with an external input (shown in black at the top of each column). Firing rates for the 50 simulated neurons. b. Poisson-generated spike times for the simulated neurons. c. Example trial showing (top) the actual (black) and inferred (cyan) input, and (bottom) actual firing rates of a subset of neurons in black and the corresponding inferred firing rates in red (bottom). d-f. Same as a-c, but for γ = 2.5, which produces significantly more chaotic dynamics than γ = 1.5. f. For this more difficult case, LFADS inferred input at the correct time (blue arrow), but also used its 1-D inferred input to shape the dynamics at times there was no actual input (green arrow).