Electroencephalography (EEG) provides high temporal resolution data that are valuable for analyzing cognitive processes, but the high noise and dimensionality make analysis difficult. Traditional event-related potential studies lose single-epoch information through epoch averaging and restricting analysis to specific landmarks. To address this, we apply a latent variable model (LVM), LFADS, to encode EEG epochs and infer lower-dimensional dynamical factors reflecting cognitive processes. We first validate LFADS on synthetic EEG data, proving it recovers latent dynamics and external inputs. We then apply LFADS to real EEG data from a reading experiment and find it can reconstruct epochs' signal and distinguish responses to words with different syntactic roles. Moreover, we decode two word features from the inferred factors, with performance comparable to decoding using components obtained from traditional dimensionality-reduction techniques. Our results illustrate the potential of dynamical LVMs as an alternative approach for EEG dimensionality reduction, preserving interpretable factors encoding cognitive information. Applying such models to clinical EEG may uncover temporal biomarkers of cognitive processes.