Hippocampal studies provide a rich window into the mechanisms of memory via the paradigm of spatial navigation. To interpret neural responses, it is common practice to first build encoding models using position during locomotion as the label, and then decode the position using this model. Of particular interest is the mismatch between the decoded and the actual position, for instance, replay of non-local trajectories during rest. However, it is unclear whether a priori chosen labels explain neural data the best. By imposing spatial structure to times of immobility, we may be systematically missing the influence of nonspatial factors. Furthermore, the encoding model requires an arbitrary separation of the running and immobility periods, making the transition between the two difficult to separate. Finally, many unsupervised models leverage smoothness to discover low-dimensional latents from noisy high-dimensional recordings. This assumption may prevent models from capturing sudden discontinuities in the latent space that may be present in the neural data. To solve these issues, we develop a latent variable model that is conceptually simple, flexible and computationally efficient. The model infers non-linear tuning of the latent states, and whether the state is smoothly varying or jumping. The expectation-maximization (EM) algorithm for fitting the model simply corresponds to iteratively applying the two steps in hippocampal studies: tuning curve estimation and label decoding. We apply this model to rodent CA1 datasets and show that learned latents explain pyramidal cell activities better than position labels. Furthermore, latent states exhibit abrupt but sustained transitions even within immobility epochs. Some of these transitions reflect transitioning in the behavioral state like movement initiation. Surprisingly, others do not have ostensible behavioral correlates. Overall, our model highlights the shortcomings of imposing external spatial labels on the cognitive map and provides a path forward to an inside-out approach to understanding hippocampal function.