On the synthetic NASCAR task, where the true generative model is an RS LDS with k=4 states and recurrent dynamics, the SLDS model (which has no recurrence) attains a reasonable test log-likelihood (1331.35) but a very high dynamical mean-squared error (0.930) between its learned state-space flow and the true flow field, compared to 0.010 for the RS LDS. The SLDS sample trajectories do not resemble the true NASCAR-track dynamics. This was checked over 5 random initialization seeds.
Evidence
correlational
Key metric
NASCAR (k=4, 5 seeds): SLDS test LL 1331.35, dyn MSE 0.930; RS LDS test LL 1628.57, dyn MSE 0.010
Caveat
The NASCAR task is synthetic and was specifically designed to test the inclusion of recurrence; the gap may be larger on this task than on other data.