Fig. 4: Prediction and generation of complex oscillatory dynamics.
From: Advancing spatio-temporal processing through adaptation in spiking neural networks
a Schematic of a 4-degree-of-freedom spring-mass system. x1 to x4 represent the displacements of the four masses. b Example displacement dynamics generated over a period of 500 ms. c Illustration of the auto-regression task. For the first 250 ms, the network received the true displacements x[k] and predict the next displacement \(\hat{{{{\boldsymbol{x}}}}}[k+1]\). After 250 ms, the model generates the displacements by using its own predictions from the previous time step in an autoregressive manner. d Displacement predictions for mass x1, by a LIF (top) and adLIF (bottom) network with 42.6K trainable parameters. e Mean squared error (MSE) in logarithmic scale during the auto-regression period for LIF, adLIF, and LSTM networks of various sizes (mean and STD over 5 unique randomly generated spring-mass systems). f Divergence of generated dynamics in the auto-regressive phase (starting after 250 ms). We report the MSE over time averaged over a 25 ms time-window. The constant model corresponds to the average MSE over time for a model that constantly predicts zero as displacement. g Mean squared error (MSE) during the auto-regression period for adLIF networks discretized with the Euler-Forward (brown) and Symplectic-Euler (pink) method on spring-mass systems with different frequency ranges.
